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class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_si.wikipedia.org&uselang=si" class=""><span>පරිත්‍යාග</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%E0%B7%80%E0%B7%92%E0%B7%81%E0%B7%9A%E0%B7%82:%E0%B6%9C%E0%B7%92%E0%B6%AB%E0%B7%94%E0%B6%B8_%E0%B6%AD%E0%B7%90%E0%B6%B1%E0%B7%93%E0%B6%B8%E0%B6%A7&returnto=%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA" title="ඔබ ගිණුමක් තනා පිවිසෙන්නේ නම් මැනවි; කෙසේ වුවත්, එය අනිවාර්ය නොවේ." class=""><span>ගිණුමක් තනන්න</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%E0%B7%80%E0%B7%92%E0%B7%81%E0%B7%9A%E0%B7%82:%E0%B6%B4%E0%B6%BB%E0%B7%92%E0%B7%81%E0%B7%93%E0%B6%BD%E0%B6%9A_%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%80%E0%B7%92%E0%B7%82%E0%B7%8A%E0%B6%A7%E0%B6%BA&returnto=%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA" title="අඩවියට පිවිසීමට ඔබව දිරිගැන්වේ. එහෙත් පිවිසීම අනිවාර්ය නොවේ. [o]" accesskey="o" class=""><span>පිවිසෙන්න</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="More options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="පුද්ගලික මෙවලම්" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">පුද්ගලික මෙවලම්</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_si.wikipedia.org&uselang=si"><span>පරිත්‍යාග</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B7%80%E0%B7%92%E0%B7%81%E0%B7%9A%E0%B7%82:%E0%B6%9C%E0%B7%92%E0%B6%AB%E0%B7%94%E0%B6%B8_%E0%B6%AD%E0%B7%90%E0%B6%B1%E0%B7%93%E0%B6%B8%E0%B6%A7&returnto=%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA" title="ඔබ ගිණුමක් තනා පිවිසෙන්නේ නම් මැනවි; කෙසේ වුවත්, එය අනිවාර්ය නොවේ."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>ගිණුමක් තනන්න</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B7%80%E0%B7%92%E0%B7%81%E0%B7%9A%E0%B7%82:%E0%B6%B4%E0%B6%BB%E0%B7%92%E0%B7%81%E0%B7%93%E0%B6%BD%E0%B6%9A_%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%80%E0%B7%92%E0%B7%82%E0%B7%8A%E0%B6%A7%E0%B6%BA&returnto=%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA" title="අඩවියට පිවිසීමට ඔබව දිරිගැන්වේ. එහෙත් පිවිසීම අනිවාර්ය නොවේ. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>පිවිසෙන්න</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/%E0%B6%8B%E0%B6%AF%E0%B7%80%E0%B7%94:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%E0%B7%80%E0%B7%92%E0%B7%81%E0%B7%9A%E0%B7%82:%E0%B6%B8%E0%B6%9C%E0%B7%9A_%E0%B6%AF%E0%B7%8F%E0%B6%BA%E0%B6%9A%E0%B6%AD%E0%B7%8A%E0%B7%80%E0%B6%BA" title="A list of edits made from this IP address [y]" accesskey="y"><span>දායකත්වයන්</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%E0%B7%80%E0%B7%92%E0%B7%81%E0%B7%9A%E0%B7%82:%E0%B6%B8%E0%B6%9C%E0%B7%9A_%E0%B7%83%E0%B7%8F%E0%B6%9A%E0%B6%A0%E0%B7%8A%E0%B6%A1%E0%B7%8F%E0%B7%80" title="මෙම අන්තර්ජාල ලිපිනයෙන් කර ඇති සංස්කරණයන් පිළිබඳ සාකච්ඡාව [n]" accesskey="n"><span>සාකච්ඡාව</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Beginning</div> </a> </li> <li id="toc-කලනයේ_මූලික_මාතෘකා" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#කලනයේ_මූලික_මාතෘකා"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>කලනයේ මූලික මාතෘකා</span> </div> </a> <button aria-controls="toc-කලනයේ_මූලික_මාතෘකා-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle කලනයේ මූලික මාතෘකා subsection</span> </button> <ul id="toc-කලනයේ_මූලික_මාතෘකා-sublist" class="vector-toc-list"> <li id="toc-අවකලනය" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#අවකලනය"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>අවකලනය</span> </div> </a> <ul id="toc-අවකලනය-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-ගුණිත_නියමය" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ගුණිත_නියමය"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>ගුණිත නියමය</span> </div> </a> <button aria-controls="toc-ගුණිත_නියමය-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle ගුණිත නියමය subsection</span> </button> <ul id="toc-ගුණිත_නියමය-sublist" class="vector-toc-list"> <li id="toc-සාධනය_කිරීම:-" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#සාධනය_කිරීම:-"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>සාධනය කිරීම:-</span> </div> </a> <ul id="toc-සාධනය_කිරීම:--sublist" class="vector-toc-list"> </ul> </li> <li id="toc-අනුකලනය" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#අනුකලනය"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>අනුකලනය</span> </div> </a> <ul id="toc-අනුකලනය-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-කලනයේ_භාවිතයන්" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#කලනයේ_භාවිතයන්"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>කලනයේ භාවිතයන්</span> </div> </a> <ul id="toc-කලනයේ_භාවිතයන්-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">කලනය</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 97 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-97" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">97 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%AB%E1%88%8D%E1%8A%A9%E1%88%88%E1%88%B5" title="ካልኩለስ – ඇම්හාරික්" lang="am" hreflang="am" data-title="ካልኩለስ" data-language-autonym="አማርኛ" data-language-local-name="ඇම්හාරික්" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Calculo" title="Calculo – ඇරගොනීස්" lang="an" hreflang="an" data-title="Calculo" data-language-autonym="Aragonés" data-language-local-name="ඇරගොනීස්" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%81%D8%A7%D8%B6%D9%84_%D9%88%D8%AA%D9%83%D8%A7%D9%85%D9%84" title="تفاضل وتكامل – අරාබි" lang="ar" hreflang="ar" data-title="تفاضل وتكامل" data-language-autonym="العربية" data-language-local-name="අරාබි" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AA%D9%81%D8%A7%D8%B6%D9%84_%D9%88%D8%AA%D9%83%D8%A7%D9%85%D9%84" title="تفاضل وتكامل – Egyptian Arabic" lang="arz" hreflang="arz" data-title="تفاضل وتكامل" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/C%C3%A1lculu" title="Cálculu – ඇස්ටියුරියන්" lang="ast" hreflang="ast" data-title="Cálculu" data-language-autonym="Asturianu" data-language-local-name="ඇස්ටියුරියන්" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Kalkulus" title="Kalkulus – Central Bikol" lang="bcl" hreflang="bcl" data-title="Kalkulus" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bg badge-Q70894304 mw-list-item" title=""><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%BE_%D0%B8_%D0%B8%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%D0%BD%D0%BE_%D1%81%D0%BC%D1%8F%D1%82%D0%B0%D0%BD%D0%B5" title="Диференциално и интегрално смятане – බල්ගේරියානු" lang="bg" hreflang="bg" data-title="Диференциално и интегрално смятане" data-language-autonym="Български" data-language-local-name="බල්ගේරියානු" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-blk mw-list-item"><a href="https://blk.wikipedia.org/wiki/%E1%80%80%E1%80%B2%E1%80%B8%E1%80%80%E1%80%AF%E1%80%9C%E1%80%90%E1%80%BA%E1%80%9E%E1%80%BA" title="ကဲးကုလတ်သ် – Pa'O" lang="blk" hreflang="blk" data-title="ကဲးကုလတ်သ်" data-language-autonym="ပအိုဝ်ႏဘာႏသာႏ" data-language-local-name="Pa'O" class="interlanguage-link-target"><span>ပအိုဝ်ႏဘာႏသာႏ</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B2%E0%A6%95%E0%A7%81%E0%A6%B2%E0%A6%BE%E0%A6%B8" title="ক্যালকুলাস – බෙංගාලි" lang="bn" hreflang="bn" data-title="ক্যালকুলাস" data-language-autonym="বাংলা" data-language-local-name="බෙංගාලි" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Infinitezimalni_ra%C4%8Dun" title="Infinitezimalni račun – බොස්නියානු" lang="bs" hreflang="bs" data-title="Infinitezimalni račun" data-language-autonym="Bosanski" data-language-local-name="බොස්නියානු" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/C%C3%A0lcul_infinitesimal" title="Càlcul infinitesimal – කැටලන්" lang="ca" hreflang="ca" data-title="Càlcul infinitesimal" data-language-autonym="Català" data-language-local-name="කැටලන්" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AC%DB%8C%D8%A7%DA%A9%D8%A7%D8%B1%DB%8C_%D9%88_%D8%AA%DB%95%D9%88%D8%A7%D9%88%DA%A9%D8%A7%D8%B1%DB%8C" title="جیاکاری و تەواوکاری – සොරානි කුර්දිෂ්" lang="ckb" hreflang="ckb" data-title="جیاکاری و تەواوکاری" data-language-autonym="کوردی" data-language-local-name="සොරානි කුර්දිෂ්" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Infinitezim%C3%A1ln%C3%AD_po%C4%8Det" title="Infinitezimální počet – චෙක්" lang="cs" hreflang="cs" data-title="Infinitezimální počet" data-language-autonym="Čeština" data-language-local-name="චෙක්" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%C4%83%D0%BB%D0%BB%D0%B0_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Математикăлла анализ – චවේෂ්" lang="cv" hreflang="cv" data-title="Математикăлла анализ" data-language-autonym="Чӑвашла" data-language-local-name="චවේෂ්" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Calcwlws" title="Calcwlws – වෙල්ෂ්" lang="cy" hreflang="cy" data-title="Calcwlws" data-language-autonym="Cymraeg" data-language-local-name="වෙල්ෂ්" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Infinitesimalregning" title="Infinitesimalregning – ඩැනිශ්" lang="da" hreflang="da" data-title="Infinitesimalregning" data-language-autonym="Dansk" data-language-local-name="ඩැනිශ්" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Infinitesimalrechnung" title="Infinitesimalrechnung – ජර්මන්" lang="de" hreflang="de" data-title="Infinitesimalrechnung" data-language-autonym="Deutsch" data-language-local-name="ජර්මන්" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Kalkulus" title="Kalkulus – Zazaki" lang="diq" hreflang="diq" data-title="Kalkulus" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-dtp mw-list-item"><a href="https://dtp.wikipedia.org/wiki/Sidsimban" title="Sidsimban – Central Dusun" lang="dtp" hreflang="dtp" data-title="Sidsimban" data-language-autonym="Kadazandusun" data-language-local-name="Central Dusun" class="interlanguage-link-target"><span>Kadazandusun</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%BF%CE%B3%CE%B9%CF%83%CE%BC%CF%8C%CF%82" title="Λογισμός – ග්‍රීක" lang="el" hreflang="el" data-title="Λογισμός" data-language-autonym="Ελληνικά" data-language-local-name="ග්‍රීක" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Calculus" title="Calculus – ඉංග්‍රීසි" lang="en" hreflang="en" data-title="Calculus" data-language-autonym="English" data-language-local-name="ඉංග්‍රීසි" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Infinitezima_kalkulo" title="Infinitezima kalkulo – එස්පැරන්ටෝ" lang="eo" hreflang="eo" data-title="Infinitezima kalkulo" data-language-autonym="Esperanto" data-language-local-name="එස්පැරන්ටෝ" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/C%C3%A1lculo_infinitesimal" title="Cálculo infinitesimal – ස්පාඤ්ඤ" lang="es" hreflang="es" data-title="Cálculo infinitesimal" data-language-autonym="Español" data-language-local-name="ස්පාඤ්ඤ" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kalkulu_infinitesimal" title="Kalkulu infinitesimal – බාස්ක්" lang="eu" hreflang="eu" data-title="Kalkulu infinitesimal" data-language-autonym="Euskara" data-language-local-name="බාස්ක්" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8%D8%A7%D9%86" title="حسابان – පර්සියානු" lang="fa" hreflang="fa" data-title="حسابان" data-language-autonym="فارسی" data-language-local-name="පර්සියානු" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Differentiaali-_ja_integraalilaskenta" title="Differentiaali- ja integraalilaskenta – ෆින්ලන්ත" lang="fi" hreflang="fi" data-title="Differentiaali- ja integraalilaskenta" data-language-autonym="Suomi" data-language-local-name="ෆින්ලන්ත" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Calcul_infinit%C3%A9simal" title="Calcul infinitésimal – ප්‍රංශ" lang="fr" hreflang="fr" data-title="Calcul infinitésimal" data-language-autonym="Français" data-language-local-name="ප්‍රංශ" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Calcalas" title="Calcalas – අයර්ලන්ත" lang="ga" hreflang="ga" data-title="Calcalas" data-language-autonym="Gaeilge" data-language-local-name="අයර්ලන්ත" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" title="微積分 – ගැන් චයිනිස්" lang="gan" hreflang="gan" data-title="微積分" data-language-autonym="贛語" data-language-local-name="ගැන් චයිනිස්" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/C%C3%A1lculo_infinitesimal" title="Cálculo infinitesimal – ගැලීසියානු" lang="gl" hreflang="gl" data-title="Cálculo infinitesimal" data-language-autonym="Galego" data-language-local-name="ගැලීසියානු" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%95%E0%AA%B2%E0%AA%A8_%E0%AA%B6%E0%AA%BE%E0%AA%B8%E0%AB%8D%E0%AA%A4%E0%AB%8D%E0%AA%B0" title="કલન શાસ્ત્ર – ගුජරාටි" lang="gu" hreflang="gu" data-title="કલન શાસ્ત્ર" data-language-autonym="ગુજરાતી" data-language-local-name="ගුජරාටි" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Calculus" title="Calculus – හෝසා" lang="ha" hreflang="ha" data-title="Calculus" data-language-autonym="Hausa" data-language-local-name="හෝසා" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/M%C3%AC-chit-f%C3%BBn-ho%CC%8Dk" title="Mì-chit-fûn-ho̍k – හකා චයිනිස්" lang="hak" hreflang="hak" data-title="Mì-chit-fûn-ho̍k" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="හකා චයිනිස්" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%A9%D7%91%D7%95%D7%9F_%D7%90%D7%99%D7%A0%D7%A4%D7%99%D7%A0%D7%99%D7%98%D7%A1%D7%99%D7%9E%D7%9C%D7%99" title="חשבון אינפיניטסימלי – හීබෲ" lang="he" hreflang="he" data-title="חשבון אינפיניטסימלי" data-language-autonym="עברית" data-language-local-name="හීබෲ" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A4%B2%E0%A4%A8" title="कलन – හින්දි" lang="hi" hreflang="hi" data-title="कलन" data-language-autonym="हिन्दी" data-language-local-name="හින්දි" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Calculus" title="Calculus – Fiji Hindi" lang="hif" hreflang="hif" data-title="Calculus" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Infinitezimalni_ra%C4%8Dun" title="Infinitezimalni račun – කෝඒෂියානු" lang="hr" hreflang="hr" data-title="Infinitezimalni račun" data-language-autonym="Hrvatski" data-language-local-name="කෝඒෂියානු" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Calculo_infinitesimal" title="Calculo infinitesimal – ඉන්ටලින්ගුආ" lang="ia" hreflang="ia" data-title="Calculo infinitesimal" data-language-autonym="Interlingua" data-language-local-name="ඉන්ටලින්ගුආ" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Kalkulus" title="Kalkulus – ඉබන්" lang="iba" hreflang="iba" data-title="Kalkulus" data-language-autonym="Jaku Iban" data-language-local-name="ඉබන්" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id badge-Q17437796 badge-featuredarticle mw-list-item" title="විශේෂාංග ලිපි"><a href="https://id.wikipedia.org/wiki/Kalkulus" title="Kalkulus – ඉන්දුනීසියානු" lang="id" hreflang="id" data-title="Kalkulus" data-language-autonym="Bahasa Indonesia" data-language-local-name="ඉන්දුනීසියානු" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Kalkulo" title="Kalkulo – ඉඩො" lang="io" hreflang="io" data-title="Kalkulo" data-language-autonym="Ido" data-language-local-name="ඉඩො" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/%C3%96rsm%C3%A6%C3%B0areikningur" title="Örsmæðareikningur – අයිස්ලන්ත" lang="is" hreflang="is" data-title="Örsmæðareikningur" data-language-autonym="Íslenska" data-language-local-name="අයිස්ලන්ත" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Calcolo_infinitesimale" title="Calcolo infinitesimale – ඉතාලි" lang="it" hreflang="it" data-title="Calcolo infinitesimale" data-language-autonym="Italiano" data-language-local-name="ඉතාලි" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%BE%AE%E5%88%86%E7%A9%8D%E5%88%86%E5%AD%A6" title="微分積分学 – ජපන්" lang="ja" hreflang="ja" data-title="微分積分学" data-language-autonym="日本語" data-language-local-name="ජපන්" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Kialkiulos" title="Kialkiulos – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Kialkiulos" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jv badge-Q17437796 badge-featuredarticle mw-list-item" title="විශේෂාංග ලිපි"><a href="https://jv.wikipedia.org/wiki/Kalkulus" title="Kalkulus – ජාවා" lang="jv" hreflang="jv" data-title="Kalkulus" data-language-autonym="Jawa" data-language-local-name="ජාවා" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%90%E1%83%9A%E1%83%99%E1%83%A3%E1%83%9A%E1%83%A3%E1%83%A1%E1%83%98" title="კალკულუსი – ජෝර්ජියානු" lang="ka" hreflang="ka" data-title="კალკულუსი" data-language-autonym="ქართული" data-language-local-name="ජෝර්ජියානු" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AF%B8%EC%A0%81%EB%B6%84%ED%95%99" title="미적분학 – කොරියානු" lang="ko" hreflang="ko" data-title="미적분학" data-language-autonym="한국어" data-language-local-name="කොරියානු" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Calculus_infinitesimalis" title="Calculus infinitesimalis – ලතින්" lang="la" hreflang="la" data-title="Calculus infinitesimalis" data-language-autonym="Latina" data-language-local-name="ලතින්" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Calculo" title="Calculo – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Calculo" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Infinitesimaalraekening" title="Infinitesimaalraekening – ලිම්බර්ගිශ්" lang="li" hreflang="li" data-title="Infinitesimaalraekening" data-language-autonym="Limburgs" data-language-local-name="ලිම්බර්ගිශ්" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Integralinis_ir_diferencialinis_skai%C4%8Diavimas" title="Integralinis ir diferencialinis skaičiavimas – ලිතුවේනියානු" lang="lt" hreflang="lt" data-title="Integralinis ir diferencialinis skaičiavimas" data-language-autonym="Lietuvių" data-language-local-name="ලිතුවේනියානු" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/R%C4%93%C4%B7ini" title="Rēķini – ලැට්වියානු" lang="lv" hreflang="lv" data-title="Rēķini" data-language-autonym="Latviešu" data-language-local-name="ලැට්වියානු" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mad mw-list-item"><a href="https://mad.wikipedia.org/wiki/Kalkulus" title="Kalkulus – මදුරීස්" lang="mad" hreflang="mad" data-title="Kalkulus" data-language-autonym="Madhurâ" data-language-local-name="මදුරීස්" class="interlanguage-link-target"><span>Madhurâ</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Kalkulus" title="Kalkulus – මිනන්ග්කබාවු" lang="min" hreflang="min" data-title="Kalkulus" data-language-autonym="Minangkabau" data-language-local-name="මිනන්ග්කබාවු" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%98%D0%BD%D1%84%D0%B8%D0%BD%D0%B8%D1%82%D0%B5%D0%B7%D0%B8%D0%BC%D0%B0%D0%BB%D0%BD%D0%BE_%D1%81%D0%BC%D0%B5%D1%82%D0%B0%D1%9A%D0%B5" title="Инфинитезимално сметање – මැසිඩෝනියානු" lang="mk" hreflang="mk" data-title="Инфинитезимално сметање" data-language-autonym="Македонски" data-language-local-name="මැසිඩෝනියානු" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B4%B2%E0%B4%A8%E0%B4%82" title="കലനം – මලයාලම්" lang="ml" hreflang="ml" data-title="കലനം" data-language-autonym="മലയാളം" data-language-local-name="මලයාලම්" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB_%D0%B1%D0%B0_%D0%B4%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB_%D1%82%D0%BE%D0%BE%D0%BB%D0%BE%D0%BB" title="Интеграл ба дифференциал тоолол – මොංගෝලියානු" lang="mn" hreflang="mn" data-title="Интеграл ба дифференциал тоолол" data-language-autonym="Монгол" data-language-local-name="මොංගෝලියානු" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%95%E0%A4%B2%E0%A4%A8" title="कलन – මරාති" lang="mr" hreflang="mr" data-title="कलन" data-language-autonym="मराठी" data-language-local-name="මරාති" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kalkulus" title="Kalkulus – මැලේ" lang="ms" hreflang="ms" data-title="Kalkulus" data-language-autonym="Bahasa Melayu" data-language-local-name="මැලේ" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%80%E1%80%B2%E1%80%80%E1%80%AF%E1%80%9C%E1%80%95%E1%80%BA" title="ကဲကုလပ် – බුරුම" lang="my" hreflang="my" data-title="ကဲကုလပ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="බුරුම" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%B2%E0%A5%8D%E0%A4%95%E0%A5%81%E0%A4%B2%E0%A4%B8" title="क्याल्कुलस – නෙවාරි" lang="new" hreflang="new" data-title="क्याल्कुलस" data-language-autonym="नेपाल भाषा" data-language-local-name="නෙවාරි" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kalkulus" title="Kalkulus – නෝර්වීජියානු නයිනෝර්ස්ක්" lang="nn" hreflang="nn" data-title="Kalkulus" data-language-autonym="Norsk nynorsk" data-language-local-name="නෝර්වීජියානු නයිනෝර්ස්ක්" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Calcul_infinitesimal" title="Calcul infinitesimal – ඔසිටාන්" lang="oc" hreflang="oc" data-title="Calcul infinitesimal" data-language-autonym="Occitan" data-language-local-name="ඔසිටාන්" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Kaalkulasii" title="Kaalkulasii – ඔරොමෝ" lang="om" hreflang="om" data-title="Kaalkulasii" data-language-autonym="Oromoo" data-language-local-name="ඔරොමෝ" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%95%E0%A9%88%E0%A8%B2%E0%A8%95%E0%A9%82%E0%A8%B2%E0%A8%B8" title="ਕੈਲਕੂਲਸ – පන්ජාබි" lang="pa" hreflang="pa" data-title="ਕੈਲਕੂਲਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="පන්ජාබි" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DA%A9%DB%8C%D9%84%DA%A9%D9%88%D9%84%D8%B3" title="کیلکولس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="کیلکولس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/C%C3%A1lculo_infinitesimal" title="Cálculo infinitesimal – පෘතුගීසි" lang="pt" hreflang="pt" data-title="Cálculo infinitesimal" data-language-autonym="Português" data-language-local-name="පෘතුගීසි" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Yupaylliy" title="Yupaylliy – ක්වීචුවා" lang="qu" hreflang="qu" data-title="Yupaylliy" data-language-autonym="Runa Simi" data-language-local-name="ක්වීචුවා" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Calcul_infinitezimal" title="Calcul infinitezimal – රොමේනියානු" lang="ro" hreflang="ro" data-title="Calcul infinitezimal" data-language-autonym="Română" data-language-local-name="රොමේනියානු" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Математический анализ – රුසියානු" lang="ru" hreflang="ru" data-title="Математический анализ" data-language-autonym="Русский" data-language-local-name="රුසියානු" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Математическай анализ – සඛා" lang="sah" hreflang="sah" data-title="Математическай анализ" data-language-autonym="Саха тыла" data-language-local-name="සඛා" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Calculus" title="Calculus – ස්කොට්ස්" lang="sco" hreflang="sco" data-title="Calculus" data-language-autonym="Scots" data-language-local-name="ස්කොට්ස්" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Infinitezimalni_ra%C4%8Dun" title="Infinitezimalni račun – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Infinitezimalni račun" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Calculus" title="Calculus – Simple English" lang="en-simple" hreflang="en-simple" data-title="Calculus" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Diferenci%C3%A1lny_a_integr%C3%A1lny_po%C4%8Det" title="Diferenciálny a integrálny počet – ස්ලෝවැක්" lang="sk" hreflang="sk" data-title="Diferenciálny a integrálny počet" data-language-autonym="Slovenčina" data-language-local-name="ස්ලෝවැක්" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Infinitezimalni_ra%C4%8Dun" title="Infinitezimalni račun – ස්ලෝවේනියානු" lang="sl" hreflang="sl" data-title="Infinitezimalni račun" data-language-autonym="Slovenščina" data-language-local-name="ස්ලෝවේනියානු" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Infinitezimalni_ra%C4%8Dun" title="Infinitezimalni račun – සර්බියානු" lang="sr" hreflang="sr" data-title="Infinitezimalni račun" data-language-autonym="Српски / srpski" data-language-local-name="සර්බියානු" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-ss mw-list-item"><a href="https://ss.wikipedia.org/wiki/Calculus" title="Calculus – ස්වති" lang="ss" hreflang="ss" data-title="Calculus" data-language-autonym="SiSwati" data-language-local-name="ස්වති" class="interlanguage-link-target"><span>SiSwati</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Infinitesimalkalkyl" title="Infinitesimalkalkyl – ස්වීඩන්" lang="sv" hreflang="sv" data-title="Infinitesimalkalkyl" data-language-autonym="Svenska" data-language-local-name="ස්වීඩන්" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AF%81%E0%AE%A3%E0%AF%8D%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="நுண்கணிதம் – දෙමළ" lang="ta" hreflang="ta" data-title="நுண்கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="දෙමළ" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%95%E0%B0%B2%E0%B0%A8_%E0%B0%97%E0%B0%A3%E0%B0%BF%E0%B0%A4%E0%B0%AE%E0%B1%81" title="కలన గణితము – තෙළිඟු" lang="te" hreflang="te" data-title="కలన గణితము" data-language-autonym="తెలుగు" data-language-local-name="තෙළිඟු" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%84%E0%B8%A5%E0%B8%84%E0%B8%B9%E0%B8%A5%E0%B8%B1%E0%B8%AA" title="แคลคูลัส – තායි" lang="th" hreflang="th" data-title="แคลคูลัส" data-language-autonym="ไทย" data-language-local-name="තායි" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Calculus" title="Calculus – Tagalog" lang="tl" hreflang="tl" data-title="Calculus" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kalk%C3%BCl%C3%BCs" title="Kalkülüs – තුර්කි" lang="tr" hreflang="tr" data-title="Kalkülüs" data-language-autonym="Türkçe" data-language-local-name="තුර්කි" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tum mw-list-item"><a href="https://tum.wikipedia.org/wiki/Kakyula" title="Kakyula – ටුම්බුකා" lang="tum" hreflang="tum" data-title="Kakyula" data-language-autonym="ChiTumbuka" data-language-local-name="ටුම්බුකා" class="interlanguage-link-target"><span>ChiTumbuka</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D1%96%D0%B0%D0%BB%D1%8C%D0%BD%D0%B5_%D1%82%D0%B0_%D1%96%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%D1%8C%D0%BD%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%BD%D1%8F" title="Диференціальне та інтегральне числення – යුක්රේනියානු" lang="uk" hreflang="uk" data-title="Диференціальне та інтегральне числення" data-language-autonym="Українська" data-language-local-name="යුක්රේනියානු" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D8%AD%D8%B5%D8%A7" title="احصا – උර්දු" lang="ur" hreflang="ur" data-title="احصا" data-language-autonym="اردو" data-language-local-name="උර්දු" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/C%C3%B3nto_infinitezima%C5%82e" title="Cónto infinitezimałe – Venetian" lang="vec" hreflang="vec" data-title="Cónto infinitezimałe" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Vi_t%C3%ADch_ph%C3%A2n" title="Vi tích phân – වියට්නාම්" lang="vi" hreflang="vi" data-title="Vi tích phân" data-language-autonym="Tiếng Việt" data-language-local-name="වියට්නාම්" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Kalkulo" title="Kalkulo – වොරෙය්" lang="war" hreflang="war" data-title="Kalkulo" data-language-autonym="Winaray" data-language-local-name="වොරෙය්" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%BE%AE%E7%A7%AF%E5%88%86%E5%AD%A6" title="微积分学 – වූ චයිනිස්" lang="wuu" hreflang="wuu" data-title="微积分学" data-language-autonym="吴语" data-language-local-name="වූ චයිනිස්" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A7%D7%90%D7%9C%D7%A7%D7%95%D7%9C%D7%95%D7%A1" title="קאלקולוס – යිඩිශ්" lang="yi" hreflang="yi" data-title="קאלקולוס" data-language-autonym="ייִדיש" data-language-local-name="යිඩිශ්" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%BE%AE%E7%A7%AF%E5%88%86%E5%AD%A6" title="微积分学 – චීන" lang="zh" hreflang="zh" data-title="微积分学" data-language-autonym="中文" data-language-local-name="චීන" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" title="微積分 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="微積分" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan 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id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="si" dir="ltr"><p><b>කලනය</b> (කලනය යන අරුත් දෙන Calculus නම් ඉංග්‍රීසි වදන, ලතින් බසෙහි Calculus යන්නෙන් ව්‍යුත්පන්න වී ඇති අතර, ගණන් කිරීමට යොදා ගන්නා කුඩා ගල් වර්ගයකි යන අදහස දෙයි.) යනු <a href="/w/index.php?title=%E0%B7%83%E0%B7%93%E0%B6%B8%E0%B7%8F_(%E0%B6%9C%E0%B6%AB%E0%B7%92%E0%B6%AD%E0%B6%BA)&action=edit&redlink=1" class="new" title="සීමා (ගණිතය) (පිටුව නොපවතියි)">සීමා</a>, <a href="/w/index.php?title=%E0%B7%81%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%92%E0%B6%AD%E0%B6%BA_(%E0%B6%9C%E0%B6%AB%E0%B7%92%E0%B6%AD%E0%B6%BA)&action=edit&redlink=1" class="new" title="ශ්‍රිතය (ගණිතය) (පිටුව නොපවතියි)">ශ්‍රිත</a>, <a href="/wiki/%E0%B7%80%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%94%E0%B6%AD%E0%B7%8A%E0%B6%B4%E0%B6%B1%E0%B7%8A%E0%B6%B1%E0%B6%BA" title="ව්‍යුත්පන්නය">ව්‍යුත්පන්න</a>, <a href="/wiki/%E0%B6%85%E0%B6%B1%E0%B7%94%E0%B6%9A%E0%B6%BD%E0%B6%BA" title="අනුකලය">අනුකල</a>, සහ <a href="/w/index.php?title=%E0%B7%81%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%9A%E0%B6%AB%E0%B7%92%E0%B6%BA_(%E0%B6%9C%E0%B6%B1%E0%B7%92%E0%B6%AD%E0%B6%BA)&action=edit&redlink=1" class="new" title="ශ්‍රේණිය (ගනිතය) (පිටුව නොපවතියි)">අපරිමිත ශ්‍රේණි</a> පිළිබඳ අධ්‍යයනය කෙරෙන <a href="/wiki/%E0%B6%9C%E0%B6%AB%E0%B7%92%E0%B6%AD%E0%B6%BA" title="ගණිතය">ගණිතයේ</a> ශාඛාවකි. මෙම විෂයය නවීන <a href="/w/index.php?title=%E0%B6%9C%E0%B6%AB%E0%B7%92%E0%B6%AD_%E0%B6%85%E0%B6%B0%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B6%B4%E0%B6%B1%E0%B6%BA&action=edit&redlink=1" class="new" title="ගණිත අධ්‍යාපනය (පිටුව නොපවතියි)">ගණිත අධ්‍යාපනයේ</a> ප්‍රධාන කොටසකි. <b><a href="/wiki/%E0%B6%85%E0%B7%80%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA" title="අවකලනය">අවකලනය</a></b> සහ <b><a href="/w/index.php?title=%E0%B6%85%E0%B6%B1%E0%B7%94%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA&action=edit&redlink=1" class="new" title="අනුකලනය (පිටුව නොපවතියි)">අනුකලනය</a></b> වශයෙන් එහි ප්‍රධාන ශාඛා දෙකක් පවතින අතර, ඒවා <a href="/w/index.php?title=%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA%E0%B7%9A_%E0%B6%B8%E0%B7%96%E0%B6%BD%E0%B7%92%E0%B6%9A_%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%B8%E0%B7%9A%E0%B6%BA%E0%B6%BA&action=edit&redlink=1" class="new" title="කලනයේ මූලික ප්‍රමේයය (පිටුව නොපවතියි)">කලනයේ මූලික ප්‍රමේයය</a> ඔස්සේ එකිනෙක හා බැ‍ඳේ. </p><p>ඉංජිනේරු විද්‍යාවේ සහ විද්‍යාවේදී කලනය බහුලව භාවිතා වන අතර වීජ ගණිතය ඇසුරෙන් පමණක් විසදිය නොහැකි ගැටළු විසදීම සදහා භාවිතා වේ. කලනය ගොඩනැගීම සදහා වීජ ගණිතය, ත්‍රිකෝණමිතිය සහ විශ්ලේෂි ජ්‍යාමිතිය බාවිතා වී ඇති අතර එයට කුලකයේ මූලික ප්‍රමේය මගින් එකිනෙකට සම්බන්ධ වී ඇති අවකලනය හා අනුකලනය නම් ප්‍රධාන කොටස් 2 ක ට අයත්ය. උසස් ගණිතයේදී කලනය, විශ්ලේෂණය යනුවෙන් හැදින්වෙන අතර ශ්‍රිතයන් පිලිබද අධ්‍යයනය ලෙස අර්ථ දැක්වේ. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="කලනයේ_මූලික_මාතෘකා"><span id=".E0.B6.9A.E0.B6.BD.E0.B6.B1.E0.B6.BA.E0.B7.9A_.E0.B6.B8.E0.B7.96.E0.B6.BD.E0.B7.92.E0.B6.9A_.E0.B6.B8.E0.B7.8F.E0.B6.AD.E0.B7.98.E0.B6.9A.E0.B7.8F"></span>කලනයේ මූලික මාතෘකා</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA&action=edit&section=1" title="ඡේදය සංස්කරණය: කලනයේ මූලික මාතෘකා"><span>සංස්කරණය</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=%E0%B6%B8%E0%B7%96%E0%B6%BD%E0%B7%92%E0%B6%9A_%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%B8%E0%B7%9A%E0%B6%BA&action=edit&redlink=1" class="new" title="මූලික ප්‍රමේය (පිටුව නොපවතියි)">මූලික ප්‍රමේය</a></li> <li><a href="/wiki/%E0%B7%81%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%92%E0%B6%AD%E0%B6%BA%E0%B6%9A_%E0%B7%83%E0%B7%93%E0%B6%B8%E0%B7%8F%E0%B7%80" title="ශ්‍රිතයක සීමාව">ශ්‍රිතයක සීමාව</a></li> <li><a href="/w/index.php?title=%E0%B7%83%E0%B7%8F%E0%B6%B1%E0%B7%8A%E0%B6%AD%E0%B6%AD%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B6%BA&action=edit&redlink=1" class="new" title="සාන්තත්‍යය (පිටුව නොපවතියි)">සාන්තත්‍යය</a></li> <li><a href="/w/index.php?title=%E0%B6%AF%E0%B7%9B%E0%B7%81%E0%B7%92%E0%B6%9A_%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA&action=edit&redlink=1" class="new" title="දෛශික කලනය (පිටුව නොපවතියි)">දෛශික කලනය</a></li> <li><a href="/w/index.php?title=%E0%B6%B1%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B6%BA_%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA&action=edit&redlink=1" class="new" title="න්‍යාය කලනය (පිටුව නොපවතියි)">න්‍යාය කලනය</a></li> <li><a href="/w/index.php?title=%E0%B6%B8%E0%B6%B0%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B6%B1%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B6%BA_%E0%B6%85%E0%B6%9C%E0%B6%BA_%E0%B6%B4%E0%B7%92%E0%B7%85%E0%B7%92%E0%B6%B6%E0%B6%AF_%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%B8%E0%B7%9A%E0%B6%BA%E0%B6%BA&action=edit&redlink=1" class="new" title="මධ්‍යන්‍යය අගය පිළිබද ප්‍රමේයය (පිටුව නොපවතියි)">මධ්‍යන්‍යය අගය පිළිබද ප්‍රමේයය</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="අවකලනය"><span id=".E0.B6.85.E0.B7.80.E0.B6.9A.E0.B6.BD.E0.B6.B1.E0.B6.BA"></span>අවකලනය</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA&action=edit&section=2" title="ඡේදය සංස්කරණය: අවකලනය"><span>සංස්කරණය</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=%E0%B6%9C%E0%B7%94%E0%B6%AB%E0%B7%92%E0%B6%AD_%E0%B6%B1%E0%B7%92%E0%B6%BA%E0%B6%B8%E0%B6%BA&action=edit&redlink=1" class="new" title="ගුණිත නියමය (පිටුව නොපවතියි)">ගුණිත නියමය</a></li> <li><a href="/w/index.php?title=%E0%B6%BD%E0%B6%B6%E0%B7%8A%E0%B6%B0%E0%B7%92_%E0%B6%B1%E0%B7%92%E0%B6%BA%E0%B6%B8%E0%B6%BA&action=edit&redlink=1" class="new" title="ලබ්ධි නියමය (පිටුව නොපවතියි)">ලබ්ධි නියමය</a></li> <li><a href="/w/index.php?title=%E0%B6%AF%E0%B7%8F%E0%B6%B8_%E0%B6%B1%E0%B7%93%E0%B6%AD%E0%B7%92%E0%B6%BA&action=edit&redlink=1" class="new" title="දාම නීතිය (පිටුව නොපවතියි)">දාම නීතිය</a></li> <li><a href="/w/index.php?title=%E0%B6%85%E0%B6%B0%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B6%9C%E0%B7%98%E0%B6%AD_%E0%B6%85%E0%B7%80%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA&action=edit&redlink=1" class="new" title="අධ්‍යාගෘත අවකලනය (පිටුව නොපවතියි)">අධ්‍යාගෘත අවකලනය</a></li> <li><a href="/w/index.php?title=%E0%B6%A7%E0%B7%9A%E0%B6%BD%E0%B6%BB%E0%B7%8A_%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%B8%E0%B7%9A%E0%B6%BA&action=edit&redlink=1" class="new" title="ටේලර් ප්‍රමේය (පිටුව නොපවතියි)">ටේලර් ප්‍රමේය</a></li> <li><a href="/w/index.php?title=%E0%B7%83%E0%B6%B8%E0%B7%8A%E0%B6%B6%E0%B6%B1%E0%B7%8A%E0%B6%B0%E0%B7%92%E0%B6%AD_%E0%B6%85%E0%B6%B1%E0%B7%94%E0%B6%B4%E0%B7%8F%E0%B6%AD&action=edit&redlink=1" class="new" title="සම්බන්ධිත අනුපාත (පිටුව නොපවතියි)">සම්බන්ධිත අනුපාත</a></li> <li><a href="/w/index.php?title=%E0%B6%85%E0%B7%80%E0%B6%9A%E0%B6%BD%E0%B6%B1_%E0%B6%BD%E0%B7%90%E0%B6%BA%E0%B7%92%E0%B7%83%E0%B7%8A%E0%B6%AD%E0%B7%94%E0%B7%80&action=edit&redlink=1" class="new" title="අවකලන ලැයිස්තුව (පිටුව නොපවතියි)">අවකලන ලැයිස්තුව</a></li> <li><a href="/w/index.php?title=%E0%B7%83%E0%B6%BB%E0%B7%8A%E0%B7%80_%E0%B7%83%E0%B7%8F%E0%B6%B8%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B6%BA%E0%B6%B1%E0%B7%8A&action=edit&redlink=1" class="new" title="සර්ව සාම්‍යයන් (පිටුව නොපවතියි)">සර්ව සාම්‍යයන්</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="ගුණිත_නියමය"><span id=".E0.B6.9C.E0.B7.94.E0.B6.AB.E0.B7.92.E0.B6.AD_.E0.B6.B1.E0.B7.92.E0.B6.BA.E0.B6.B8.E0.B6.BA"></span>ගුණිත නියමය</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA&action=edit&section=3" title="ඡේදය සංස්කරණය: ගුණිත නියමය"><span>සංස්කරණය</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>x විශයයයෙන් අවකල්‍ය ශ්‍රිත දෙකක ගුණිතය අවකලනය කරන ආකාරය සලකා බලමු.<br /> u හා v යනු xහි අවකල්‍ය ශ්‍රිත 2ක් වන විට,<br /> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d(uv)}{dx}}=u{\frac {dv}{dx}}+v{\frac {du}{dx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mi>v</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>v</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>u</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d(uv)}{dx}}=u{\frac {dv}{dx}}+v{\frac {du}{dx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d4737388e833714f0f6085108addb2f23af8d09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.478ex; height:5.843ex;" alt="{\displaystyle {\frac {d(uv)}{dx}}=u{\frac {dv}{dx}}+v{\frac {du}{dx}}}"></span><br /> <dl><dd>ලෙස පද දෙකේ ගුණිත පදය අවකලනය කළ හැකිය.</dd></dl></dd></dl> <div class="mw-heading mw-heading5"><h5 id="සාධනය_කිරීම:-"><span id=".E0.B7.83.E0.B7.8F.E0.B6.B0.E0.B6.B1.E0.B6.BA_.E0.B6.9A.E0.B7.92.E0.B6.BB.E0.B7.93.E0.B6.B8:-"></span>සාධනය කිරීම:-</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA&action=edit&section=4" title="ඡේදය සංස්කරණය: සාධනය කිරීම:-"><span>සංස්කරණය</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=uv\qquad (1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>u</mi> <mi>v</mi> <mspace width="2em" /> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=uv\qquad (1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6adb46861ce16fc0d3475342e7da950eac3f98a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.328ex; height:2.843ex;" alt="{\displaystyle y=uv\qquad (1)}"></span></dd></dl> <p>යැයි ගනිමු.<br /> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> හි <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d22318bef6d7358b79bd993321d65d7c1d3db9d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.378ex; height:2.343ex;" alt="{\displaystyle \delta x}"></span> වෘදිධියට අනුරූප <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span>,<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> හා <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span> හි වෘද්ධීන් <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1dc454b7f0e03259e9c5e8568fcef1c8e6b78230" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.204ex; height:2.676ex;" alt="{\displaystyle \delta y}"></span>,<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3d3a9f07afe317da6c69b47a5fadcc58bf69d4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.378ex; height:2.343ex;" alt="{\displaystyle \delta u}"></span> හා <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd7e11c9eeacc5b5a590702ebf9067f68546d6c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.176ex; height:2.343ex;" alt="{\displaystyle \delta v}"></span> නම්,<br /> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y+\delta y=(u+\delta u)(v+\delta v)\qquad (2)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>+</mo> <mi>δ</mi> <mi>y</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo>+</mo> <mi>δ</mi> <mi>u</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>v</mi> <mo>+</mo> <mi>δ</mi> <mi>v</mi> <mo stretchy="false">)</mo> <mspace width="2em" /> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y+\delta y=(u+\delta u)(v+\delta v)\qquad (2)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e40f95abd0c1275d008e83184eae99bb569134f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.227ex; height:2.843ex;" alt="{\displaystyle y+\delta y=(u+\delta u)(v+\delta v)\qquad (2)}"></span></dd></dl> <p>(02)-(01) න්,<br /> </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\delta y&=uv+u\delta v+v\delta u+\delta u\delta v-uv\\&=u\delta v+v\delta u+\delta u\delta v\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>δ</mi> <mi>y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>u</mi> <mi>v</mi> <mo>+</mo> <mi>u</mi> <mi>δ</mi> <mi>v</mi> <mo>+</mo> <mi>v</mi> <mi>δ</mi> <mi>u</mi> <mo>+</mo> <mi>δ</mi> <mi>u</mi> <mi>δ</mi> <mi>v</mi> <mo>−</mo> <mi>u</mi> <mi>v</mi> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>u</mi> <mi>δ</mi> <mi>v</mi> <mo>+</mo> <mi>v</mi> <mi>δ</mi> <mi>u</mi> <mo>+</mo> <mi>δ</mi> <mi>u</mi> <mi>δ</mi> <mi>v</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\delta y&=uv+u\delta v+v\delta u+\delta u\delta v-uv\\&=u\delta v+v\delta u+\delta u\delta v\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acf12aab4a0d95ce4d959360f7e4b97d534ff215" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:33.897ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}\delta y&=uv+u\delta v+v\delta u+\delta u\delta v-uv\\&=u\delta v+v\delta u+\delta u\delta v\end{aligned}}}"></span></dd></dl></dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d22318bef6d7358b79bd993321d65d7c1d3db9d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.378ex; height:2.343ex;" alt="{\displaystyle \delta x}"></span> වලින් බෙදු විට,<br /> </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}{\frac {\delta y}{\delta x}}&=u{\frac {\delta v}{\delta x}}+v{\frac {\delta u}{\delta x}}+{\frac {\delta u\delta v}{\delta x}}\\\lim \limits _{\delta x\to 0}{\frac {\delta y}{\delta x}}&=\lim \limits _{\delta x\to 0}\left(u{\frac {\delta v}{\delta x}}+v{\frac {\delta u}{\delta x}}+{\frac {\delta u\delta v}{\delta x}}\right)\\&=u\lim \limits _{\delta x\to 0}{\frac {\delta v}{\delta x}}+v\lim \limits _{\delta x\to 0}{\frac {\delta u}{\delta x}}+\lim \limits _{\delta x\to 0}{\frac {\delta u\delta v}{\delta x}}\\\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>y</mi> </mrow> <mrow> <mi>δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>v</mi> </mrow> <mrow> <mi>δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>u</mi> </mrow> <mrow> <mi>δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>u</mi> <mi>δ</mi> <mi>v</mi> </mrow> <mrow> <mi>δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <munder> <mo form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>δ</mi> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>y</mi> </mrow> <mrow> <mi>δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <munder> <mo form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>δ</mi> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow> <mo>(</mo> <mrow> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>v</mi> </mrow> <mrow> <mi>δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>u</mi> </mrow> <mrow> <mi>δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>u</mi> <mi>δ</mi> <mi>v</mi> </mrow> <mrow> <mi>δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>u</mi> <munder> <mo form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>δ</mi> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>v</mi> </mrow> <mrow> <mi>δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>v</mi> <munder> <mo form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>δ</mi> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>u</mi> </mrow> <mrow> <mi>δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <munder> <mo form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>δ</mi> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>δ</mi> <mi>u</mi> <mi>δ</mi> <mi>v</mi> </mrow> <mrow> <mi>δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\frac {\delta y}{\delta x}}&=u{\frac {\delta v}{\delta x}}+v{\frac {\delta u}{\delta x}}+{\frac {\delta u\delta v}{\delta x}}\\\lim \limits _{\delta x\to 0}{\frac {\delta y}{\delta x}}&=\lim \limits _{\delta x\to 0}\left(u{\frac {\delta v}{\delta x}}+v{\frac {\delta u}{\delta x}}+{\frac {\delta u\delta v}{\delta x}}\right)\\&=u\lim \limits _{\delta x\to 0}{\frac {\delta v}{\delta x}}+v\lim \limits _{\delta x\to 0}{\frac {\delta u}{\delta x}}+\lim \limits _{\delta x\to 0}{\frac {\delta u\delta v}{\delta x}}\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e93e8ae6d92caafdd010bcecda0bce47e59529c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.171ex; width:45.932ex; height:17.509ex;" alt="{\displaystyle {\begin{aligned}{\frac {\delta y}{\delta x}}&=u{\frac {\delta v}{\delta x}}+v{\frac {\delta u}{\delta x}}+{\frac {\delta u\delta v}{\delta x}}\\\lim \limits _{\delta x\to 0}{\frac {\delta y}{\delta x}}&=\lim \limits _{\delta x\to 0}\left(u{\frac {\delta v}{\delta x}}+v{\frac {\delta u}{\delta x}}+{\frac {\delta u\delta v}{\delta x}}\right)\\&=u\lim \limits _{\delta x\to 0}{\frac {\delta v}{\delta x}}+v\lim \limits _{\delta x\to 0}{\frac {\delta u}{\delta x}}+\lim \limits _{\delta x\to 0}{\frac {\delta u\delta v}{\delta x}}\\\end{aligned}}}"></span></dd></dl></dd></dl> <p>එමනිසා <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {dy}{dx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dy}{dx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ceb16b58a91d26cf1e442d0682dfa7a2c0ab72c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:3.382ex; height:5.509ex;" alt="{\displaystyle {\frac {dy}{dx}}}"></span> අර්ථ දැක්වීම අනූව </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {dy}{dx}}=u{\frac {dv}{dx}}+v{\frac {du}{dx}}+0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>v</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>u</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dy}{dx}}=u{\frac {dv}{dx}}+v{\frac {du}{dx}}+0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fad7b6322d7b32e5f755f71cc6623e2260484696" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:22.544ex; height:5.509ex;" alt="{\displaystyle {\frac {dy}{dx}}=u{\frac {dv}{dx}}+v{\frac {du}{dx}}+0}"></span> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {dy}{dx}}=u{\frac {dv}{dx}}+v{\frac {du}{dx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>v</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>u</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dy}{dx}}=u{\frac {dv}{dx}}+v{\frac {du}{dx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8d6eda3f3808c58c997d652910447e57e541fd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:18.541ex; height:5.509ex;" alt="{\displaystyle {\frac {dy}{dx}}=u{\frac {dv}{dx}}+v{\frac {du}{dx}}}"></span></dd></dl></dd></dl></dd></dl></dd></dl> <div class="mw-heading mw-heading3"><h3 id="අනුකලනය"><span id=".E0.B6.85.E0.B6.B1.E0.B7.94.E0.B6.9A.E0.B6.BD.E0.B6.B1.E0.B6.BA"></span>අනුකලනය</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA&action=edit&section=5" title="ඡේදය සංස්කරණය: අනුකලනය"><span>සංස්කරණය</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>අනුකල ලැයිස්තුව</li> <li>විෂම අනුකල</li> <li>කොටස් වශයෙන් අනුකලනය</li> <li>තැටි ලෙස අනුකලනය</li> <li>සිලින්ඩර් ලෙස අනුකලනය</li> <li>කවච ලෙස අනුකලනය</li> <li>ආදේශක අනුකලනය</li> <li>ත්‍රිකෝණමිතික ආදේශක අනුකලනය</li> <li>භින්න භාග</li></ul> <div class="mw-heading mw-heading2"><h2 id="කලනයේ_භාවිතයන්"><span id=".E0.B6.9A.E0.B6.BD.E0.B6.B1.E0.B6.BA.E0.B7.9A_.E0.B6.B7.E0.B7.8F.E0.B7.80.E0.B7.92.E0.B6.AD.E0.B6.BA.E0.B6.B1.E0.B7.8A"></span>කලනයේ භාවිතයන්</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA&action=edit&section=6" title="ඡේදය සංස්කරණය: කලනයේ භාවිතයන්"><span>සංස්කරණය</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%E0%B6%9C%E0%B7%9C%E0%B6%B1%E0%B7%94%E0%B7%80:NautilusCutawayLogarithmicSpiral.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/NautilusCutawayLogarithmicSpiral.jpg/220px-NautilusCutawayLogarithmicSpiral.jpg" decoding="async" width="220" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/NautilusCutawayLogarithmicSpiral.jpg/330px-NautilusCutawayLogarithmicSpiral.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/08/NautilusCutawayLogarithmicSpiral.jpg/440px-NautilusCutawayLogarithmicSpiral.jpg 2x" data-file-width="2240" data-file-height="1693" /></a><figcaption>කලනය සමග බැදි ඇති වර්ධනයක් හා විචලනයන් නිරූපණය කිරීම සදහා Nautilus කවචයේ ලඝුගණක සර්පිල ස්වරූපය දැක්වෙන රූප අතීතයේ සිටම භාවිතා විය.</figcaption></figure> <p>ගැටළුවක් ගණිතමය ලෙස ආදර්ශනය කල හැකි වන්න‍‍ා වුත්, ප්‍රශංසී විසදුමක් බලාපොරොත්තු වන්නා වූත් ඕනෑම ක්ෂේත්‍රයක් සඳහා කලනය යොදා ගත හැක. මේ අතරට පරිගණක විද්‍යාව සංඛ්‍යාතය, ඉන්ජිනේරු විද්‍යාව, ආර්ථික විද්‍යාව වෙළඳාම සහ වෛද්‍ය විද්‍යාව ආදි වු ස්වභාව විද්‍යාවන්ට අයත් සියළුම ක්ෂේත්‍ර අයත් වේ. </p><p>මේ අතරින් භෞතික විද්‍යාවේදී කලනය විශේෂයෙන් භාවිතා වේ. ප්‍රතිස්ඨිත/පැරණි භෞතික විද්‍යාවේ සියළු සංකල්ප කලනය ඔස්සේ අන්තර්සම්බන්ධිත වේ. ඝනත්වය දන්නා වස්තුවක ස්කන්ධය, වස්තූන්ගේ ආවස්ථිති ඝුර්ණය මෙන්ම සංස්ථිති ක්ෂේත්‍රයක් තුළ අන්තර්ගත වස්තුවක ශක්තියද කලනය අසුරින් ගණනය කල හැක. විද්‍යුතය සහ චුම්භකත්වය පිළිබඳ උපක්ෂේත්‍ර වලදී විද්‍යුත් චුම්භක ක්ෂේත්‍ර වලදී සම්පුර්ණ ස්‍රාවය සෙවීම සඳහා කලනය යොදා ගත හැක. තවද කලනයේ භාවිතය සදහා වඩාත් ඓතිහාසික උදාහරණයක් වන්නේ “විචලන සීඝ්‍රතාව” පිලිබඳ සෘජුව ප්‍රකාශ කරන නිව්ටන්ගේ චලිතය පිළිබඳ දෙවැනි නියමයයි. ඉන් කියවෙන්නේ වස්තුවක ගම්‍යතාව “වෙනස් වීමේ සීඝ්‍රතාව එය මත ක්‍රියාකල බලයට සමාන වන අතර ගම්‍යතාව වෙනස් වන දිශාව බලයේ දිශාව ඔස්සේම වේ” යන්නයි. එමෙන්ම ත්වරණය, ප්‍රවේගයේ ව්‍යුත්පන්නයක් සේ ප්‍රකාශ කළ හැකි බැවින් නිව්ටන්ගේ දෙවැනි නියමය ප්‍රකාශ කරන සාමාන්‍ය ආකාරය මත බලය = ස්කන්ධය x ත්වරණය(F=ma) යන සමීකරණයේද අවකලනය අන්තර්ගත වේ. මැක්ස්වෙල්ගේ විද්‍යුත්චුම්භකත්වය පිළිබඳ වාදය සහ අයින්ස්ටයින්ගේ සාමාන්‍ය සාපේක්ෂවාදය පවා ප්‍රකාශ කෙරෙනුයේ අවකලනය භාවිතයෙනි. විකිරණශීලි ක්ෂ්‍යවීමේ සීඝ්‍රතාවක් සහ ප්‍රතික්‍රියා සීඝ්‍රතා තිරණය කිරීම සඳහා රසායන විද්‍යාවේදී කලනය ප්‍රයෝජනවත් වේ. </p><p>කලනය වෙනත් ගණිතමය සංකල්ප සමග එක්ව යොදා ගැනීමද කළ හැකි අතර වසමකට අයත් ලක්ෂ කලකයක් සඳහා රේඛීය සන්නිකර්ෂණයේ සුදුසුතම අනුසීනුව සොයා ගැනීම සඳහා රේඛීය වීජ ගණිතයේදී කලනයේ භාවිතයන් මෙවන් අවස්ථාවකට උදාහරණයකි. </p><p>වෛද්‍ය විද්‍ය‍ාවේදී ලේ ගමණාගමනය උපරිම වීම සඳහා රුධිර වාහිණියක් සතුවිය යුතු ප්‍රසංගී ශාඛක කෝණය ගණනය කිරීම සඳහා කලනය යොදා ගත හැක. විශ්ලේෂි ජ්‍යාමිතියේ ශ්‍රිතයන් ප්‍රස්ථාරවල උපරිම හා අවම ලක්ෂයන්‍, බෑවුම, අවකලතාව සහ නතිවර්තන ලක්ෂ සෙවීම සඳහා කලනය යොදා ගැනේ. </p><p>ආර්ථික විද්‍යාවේදී කලනය ආන්තික වියදම සහ ආන්තික බදු ප්‍රමාණය ගණනය කිරීමට පහසු ක්‍රමයක් සැලසීම මගින් උපරිම ලාභය ගණනය කිරීමට ඉඩ සලසයි. </p><p>නිව්ටන් ක්‍රමය, අචල ලක්ෂ ප්‍රතඃකරණය සහ රේඛීය සන්නිකර්ෂණය වැනි ක්‍රමයේදී සමීකරණ සඳහා සන්නිකර්ෂණ විසදුම් ගණනය කිරීම සඳහා කලනය යොදාගත හැක. උදාහරණයක් ලෙස අභ්‍යවකාශ යානා සඳහා ශුන්‍ය ගුරුත්ව අවකාශ තල වක්‍රාකාර ගමන්පත් සන්නිකර්ෂණය කිරීමට ඉයුලර් ක්‍රමයේ එක් ආකාරයක් යොදා ගැනීම පෙන්වාදිය හැක. </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div 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