∂ – Wikipedia

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</span> </a> </div> <form action="/w/index.php" method="get" class="minerva-search-form"> <div class="search-box"><input type="hidden" name="title" value="Spezial:Suche"> <input class="search skin-minerva-search-trigger" id="searchInput" type="search" name="search" placeholder="Wikipedia durchsuchen" aria-label="Wikipedia durchsuchen" autocapitalize="sentences" title="Durchsuche die Wikipedia [f]" accesskey="f"> <span class="search-box-icon-overlay"><span class="minerva-icon minerva-icon--search"></span> </span> </div><button id="searchIcon" class="cdx-button cdx-button--size-large cdx-button--icon-only cdx-button--weight-quiet skin-minerva-search-trigger"> <span class="minerva-icon minerva-icon--search"></span> <span>Suchen</span> </button> </form> <nav class="minerva-user-navigation" aria-label="Weitere Navigation"> </nav> </div> </header> <main id="content" class="mw-body"> <div class="banner-container"> <div id="siteNotice"></div> </div> <div class="pre-content heading-holder"> <div class="page-heading"> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">∂</span></h1> <div class="tagline"> mathematisches Symbol </div> </div> <ul id="p-associated-pages" class="minerva__tab-container"> <li class="minerva__tab selected"><a class="minerva__tab-text" href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" rel="" data-event-name="tabs.subject">Artikel</a></li> <li class="minerva__tab new"><a class="minerva__tab-text" href="https://de-m-wikipedia-org.translate.goog/w/index.php?title=Diskussion:%E2%88%82&action=edit&redlink=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" rel="discussion" data-event-name="tabs.talk">Diskussion</a></li> </ul> <nav class="page-actions-menu"> <ul id="p-views" class="page-actions-menu__list"> <li id="language-selector" class="page-actions-menu__list-item"><a role="button" 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rahmenfarbe1 navigation-not-searchable noprint hatnote navigation-not-searchable" style="border-bottom-style: solid; border-bottom-width: 1px; font-size:95%; margin-bottom:1em; padding: 0.25em; overflow: hidden; word-break: break-word; word-wrap: break-word;" id="Vorlage_Dieser_Artikel"> <div class="noviewer noresize" style="display: table-cell; padding-bottom: 0.2em; padding-left: 0.25em; padding-right: 1em; padding-top: 0.2em; vertical-align: middle;" id="bksicon" aria-hidden="true" role="presentation"> <span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Disambig-dark.svg/25px-Disambig-dark.svg.png" decoding="async" width="25" height="19" class="mw-file-element" srcset="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Disambig-dark.svg/38px-Disambig-dark.svg.png 1.5x,https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Disambig-dark.svg/50px-Disambig-dark.svg.png 2x" data-file-width="444" data-file-height="340"></span></span> </div> <div style="display: table-cell; vertical-align: middle; width: 100%;"> <div role="navigation"> Dieser Artikel behandelt das mathematische Symbol. Zum kyrillischen Buchstaben <i>д</i> siehe <a href="https://de-m-wikipedia-org.translate.goog/wiki/%D0%94?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Д">Д</a>, zum griechischen Buchstaben δ siehe <a href="https://de-m-wikipedia-org.translate.goog/wiki/Delta?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Delta">Delta</a>, zum Buchstaben ꝺ siehe <a href="https://de-m-wikipedia-org.translate.goog/wiki/Insulare_Schriften?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Insulare Schriften">Insulare Schriften</a>. </div> </div> </div> <table class="wikitable float-right"> <tbody> <tr> <th colspan="2"> <div class="punctuation" style="text-align:center; font-size:800%; line-height:1em; padding:0 0.25em"> ∂ </div></th> </tr> <tr> <th colspan="2"><a href="https://de-m-wikipedia-org.translate.goog/wiki/Liste_mathematischer_Symbole?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Liste mathematischer Symbole">Mathematische Zeichen</a></th> </tr> <tr> <th colspan="2">Arithmetik</th> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Pluszeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Pluszeichen">Pluszeichen</a></td> <td align="center">+</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Minuszeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Minuszeichen">Minuszeichen</a></td> <td align="center">−, ⁒</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Malzeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Malzeichen">Malzeichen</a></td> <td align="center">⋅, ×</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Geteiltzeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Geteiltzeichen">Geteiltzeichen</a></td> <td align="center">:, ÷, /</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Plusminuszeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Plusminuszeichen">Plusminuszeichen</a></td> <td align="center">±, ∓</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Vergleichszeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Vergleichszeichen">Vergleichszeichen</a></td> <td align="center"><, ≤, =, ≥, ></td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Wurzelzeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Wurzelzeichen">Wurzelzeichen</a></td> <td align="center">√</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Prozentzeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Prozentzeichen">Prozentzeichen</a></td> <td align="center">%</td> </tr> <tr> <th colspan="2">Analysis</th> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Summe?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Notation_mit_dem_Summenzeichen" title="Summe">Summenzeichen</a></td> <td align="center">Σ</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Produkt_(Mathematik)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Endliche_und_unendliche_Produkte" title="Produkt (Mathematik)">Produktzeichen</a></td> <td align="center">Π</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Differenzzeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Differenzzeichen">Differenzzeichen</a>, <a href="https://de-m-wikipedia-org.translate.goog/wiki/Nabla?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Nabla">Nabla</a></td> <td align="center">∆, ∇</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Prime_(Typografie)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Prime (Typografie)">Prime</a></td> <td align="center">′</td> </tr> <tr> <td><a class="mw-selflink selflink">Partielles Differential</a></td> <td align="center">∂</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Integralzeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Integralzeichen">Integralzeichen</a></td> <td align="center">∫</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Verkettungszeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Verkettungszeichen">Verkettungszeichen</a></td> <td align="center">∘</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Unendlichzeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Unendlichzeichen">Unendlichzeichen</a></td> <td align="center">∞</td> </tr> <tr> <th colspan="2">Geometrie</th> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Winkel?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Bezeichnung_von_Winkeln" title="Winkel">Winkelzeichen</a></td> <td align="center">∠, ∡, ∢, ∟</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Orthogonalit%C3%A4t?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Orthogonalität">Senkrecht</a>, <a href="https://de-m-wikipedia-org.translate.goog/wiki/Parallelit%C3%A4t_(Geometrie)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Parallelität (Geometrie)">Parallel</a></td> <td align="center">⊥, ∥</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Dreieck?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Dreieck">Dreieck</a>, <a href="https://de-m-wikipedia-org.translate.goog/wiki/Viereck?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Viereck">Viereck</a></td> <td align="center">△, □</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Durchmesserzeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Durchmesserzeichen">Durchmesserzeichen</a></td> <td align="center">⌀</td> </tr> <tr> <th colspan="2">Mengenlehre</th> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Menge_(Mathematik)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Vereinigung_(Vereinigungsmenge)" title="Menge (Mathematik)">Vereinigung</a>, <a href="https://de-m-wikipedia-org.translate.goog/wiki/Menge_(Mathematik)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Durchschnitt_(Schnittmenge,_Schnitt)" title="Menge (Mathematik)">Schnitt</a></td> <td align="center">∪, ∩</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Menge_(Mathematik)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Differenz_und_Komplement" title="Menge (Mathematik)">Differenz</a>, <a href="https://de-m-wikipedia-org.translate.goog/wiki/Komplement_(Mengenlehre)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Komplement (Mengenlehre)">Komplement</a></td> <td align="center">∖, ∁</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Elementzeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Elementzeichen">Elementzeichen</a></td> <td align="center">∈</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Teilmenge?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Teilmenge">Teilmenge</a>, <a href="https://de-m-wikipedia-org.translate.goog/wiki/Teilmenge?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Teilmenge">Obermenge</a></td> <td align="center">⊂, ⊆, ⊇, ⊃</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Leere_Menge?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Leere Menge">Leere Menge</a></td> <td align="center">∅</td> </tr> <tr> <th colspan="2">Logik</th> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Folgepfeil?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Folgepfeil">Folgepfeil</a></td> <td align="center">⇒, ⇔, ⇐</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Quantor?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Quantor">Allquantor</a></td> <td align="center">∀</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Quantor?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Quantor">Existenzquantor</a></td> <td align="center">∃</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Konjunktion_(Logik)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Konjunktion (Logik)">Konjunktion</a>, <a href="https://de-m-wikipedia-org.translate.goog/wiki/Disjunktion?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Disjunktion">Disjunktion</a></td> <td align="center">∧, ∨</td> </tr> <tr> <td><a href="https://de-m-wikipedia-org.translate.goog/wiki/Negationszeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Negationszeichen">Negationszeichen</a></td> <td align="center">¬</td> </tr> </tbody> </table> <p>Das <b>∂</b> (sprich: <b>Del</b>) ist ein <a href="https://de-m-wikipedia-org.translate.goog/wiki/Liste_mathematischer_Symbole?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Liste mathematischer Symbole">mathematisches Symbol</a>, das hauptsächlich für die <a href="https://de-m-wikipedia-org.translate.goog/wiki/Partielle_Ableitung?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Partielle Ableitung">partielle Ableitung</a> <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 {\tfrac {\partial }{\partial x}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi mathvariant="normal"> ∂ </mi> <mrow> <mi mathvariant="normal"> ∂ </mi> <mi> x </mi> </mrow> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\tfrac {\partial }{\partial x}}} </annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fccdcb2675c59725c4a200e3f4f2c270497c17b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.708ex; height:3.843ex;" alt="{\displaystyle {\tfrac {\partial }{\partial x}}}"></span> und das partielle <a href="https://de-m-wikipedia-org.translate.goog/wiki/Differential_(Mathematik)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Differential (Mathematik)">Differential</a> <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 \partial f}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal"> ∂ </mi> <mi> f </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle \partial f} </annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e49e78bca168615a85789d3cbf71bb206b66430" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.597ex; height:2.509ex;" alt="{\displaystyle \partial f}"></span> benutzt wird. Es hat die <a href="https://de-m-wikipedia-org.translate.goog/wiki/Unicode?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Unicode">Unicodenummer</a> <a href="https://de-m-wikipedia-org.translate.goog/wiki/Unicodeblock_Mathematische_Operatoren?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Unicodeblock Mathematische Operatoren">U+2202</a>.<sup id="cite_ref-1" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></p> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"> <input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none"> <div class="toctitle" lang="de" dir="ltr"> <h2 id="mw-toc-heading">Inhaltsverzeichnis</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span> </div> <ul> <li class="toclevel-1 tocsection-1"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Namen"><span class="tocnumber">1</span> <span class="toctext">Namen</span></a></li> <li class="toclevel-1 tocsection-2"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Verwendungsgeschichte"><span class="tocnumber">2</span> <span class="toctext">Verwendungsgeschichte</span></a></li> <li class="toclevel-1 tocsection-3"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Anwendungen"><span class="tocnumber">3</span> <span class="toctext">Anwendungen</span></a></li> <li class="toclevel-1 tocsection-4"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Kodierung"><span class="tocnumber">4</span> <span class="toctext">Kodierung</span></a></li> <li class="toclevel-1 tocsection-5"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Weblink"><span class="tocnumber">5</span> <span class="toctext">Weblink</span></a></li> <li class="toclevel-1 tocsection-6"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Quellen"><span class="tocnumber">6</span> <span class="toctext">Quellen</span></a></li> </ul> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(1)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Namen">Namen</h2><span class="mw-editsection"> <a role="button" href="https://de-m-wikipedia-org.translate.goog/w/index.php?title=%E2%88%82&action=edit&section=1&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Abschnitt bearbeiten: Namen" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>Bearbeiten</span> </a> </span> </div> <section class="mf-section-1 collapsible-block" id="mf-section-1"> <p>Der geläufigste Name des ∂ ist <i>Del</i>,<sup id="cite_ref-2" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> was allerdings im Englischen auch den <a href="https://de-m-wikipedia-org.translate.goog/wiki/Nabla-Operator?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Nabla-Operator">Nabla-Operator</a> bezeichnet. Daher gibt es weitere Namen für das Symbol, u. a. <i>partielles d</i>,<sup id="cite_ref-4" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> im Englischen <i>Dabba</i><sup id="cite_ref-5" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> oder <i>Jacobidelta</i>,<sup id="cite_ref-Aldrich_6-0" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-Aldrich-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> sowie einfach <i>d</i>.<sup id="cite_ref-7" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Dann ist es allerdings sprachlich nicht mehr von der <a href="https://de-m-wikipedia-org.translate.goog/wiki/Totales_Differential?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Totales Differential">totalen Ableitung</a> zu unterscheiden.</p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(2)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Verwendungsgeschichte">Verwendungsgeschichte</h2><span class="mw-editsection"> <a role="button" href="https://de-m-wikipedia-org.translate.goog/w/index.php?title=%E2%88%82&action=edit&section=2&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Abschnitt bearbeiten: Verwendungsgeschichte" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>Bearbeiten</span> </a> </span> </div> <section class="mf-section-2 collapsible-block" id="mf-section-2"> <p>So wie das <a href="https://de-m-wikipedia-org.translate.goog/wiki/Integralzeichen?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Integralzeichen">Integralzeichen</a> eine spezielle Form des <a href="https://de-m-wikipedia-org.translate.goog/wiki/Langes_s?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Langes s">langen s</a> darstellt, ist das ∂ eine spezielle kursive Schreibweise des <i>d</i>s. Zuerst verwendet wurde es 1770 vom französischen Mathematiker <a href="https://de-m-wikipedia-org.translate.goog/wiki/Marie_Jean_Antoine_Nicolas_Caritat,_Marquis_de_Condorcet?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Marie Jean Antoine Nicolas Caritat, Marquis de Condorcet">Nicolas de Concordet</a> als Symbol für das partielle Differential.<sup id="cite_ref-Aldrich_6-1" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-Aldrich-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></p> <div class="Vorlage_Zitat" style="margin:1em 40px;"> <div style="margin:1em 0;"> <blockquote style="margin:0;"> <p>„Dans toute la suite de ce Memoire, dz & ∂z désigneront ou deux differences partielles de z, dont une par rapport a x, l'autre par rapport a y, ou bien dz sera une différentielle totale, & ∂z une difference partielle.“</p> </blockquote> <blockquote style="margin:.5em 0 0 0;" lang="de-Latn"> <p>„Im weiteren Verlauf dieser Abhandlung bezeichnen dz & ∂z entweder zwei partielle Differentiale von z, davon einer in Bezug auf x, der andere in Bezug auf y, oder dz ist ein Gesamtdifferential & ∂z ein partielles Differential.“</p> </blockquote> </div> <div class="cite" style="margin:-1em 0 1em 1em;"> – <style data-mw-deduplicate="TemplateStyles:r181095833">.mw-parser-output .Person{font-variant:small-caps}</style><span class="Person h-card"><a href="https://de-m-wikipedia-org.translate.goog/wiki/Marie_Jean_Antoine_Nicolas_Caritat,_Marquis_de_Condorcet?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Marie Jean Antoine Nicolas Caritat, Marquis de Condorcet">Antoine-Nicolas Caritat, Marquis de Condorcet</a></span>: <cite style="font-style:normal"><i>Memoire sur les Equations aux différence partielles</i>, 1773<sup id="cite_ref-8" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></cite> </div> </div> <p><a href="https://de-m-wikipedia-org.translate.goog/wiki/Adrien-Marie_Legendre?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Adrien-Marie Legendre">Adrien-Marie Legendre</a> verwendete es 1786 erstmals für die partielle Ableitung.<sup id="cite_ref-Aldrich_6-2" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-Aldrich-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></p> <div class="Vorlage_Zitat" style="margin:1em 40px;"> <div style="margin:1em 0;"> <blockquote style="margin:0;"> <p>„Pour éviter toute ambiguité, je représenterai par ∂u/∂x le coefficient de x dans la différence de u, & par du/dx la différence complète de u divisée par dx.“</p> </blockquote> <blockquote style="margin:.5em 0 0 0;" lang="de-Latn"> <p>„Um Mehrdeutigkeiten zu vermeiden, werde ich durch ∂u/∂x den Koeffizienten von x im Differential von u & durch du/dx das totale Differential von u geteilt durch dx darstellen.“</p> </blockquote> </div> <div class="cite" style="margin:-1em 0 1em 1em;"> – <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r181095833"><span class="Person h-card"><a href="https://de-m-wikipedia-org.translate.goog/wiki/Adrien-Marie_Legendre?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Adrien-Marie Legendre">Adrien-Marie Legendre</a></span>: <cite style="font-style:normal"><i>Memoire sur la manière de distinguer les maxima des minima dans le Calcul des Variations</i>, 1786<sup id="cite_ref-9" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></cite> </div> </div> <p>Legendre stellte die Verwendung später ein. <a href="https://de-m-wikipedia-org.translate.goog/wiki/Carl_Gustav_Jacob_Jacobi?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Carl Gustav Jacob Jacobi">Carl Gustav Jacob Jacobi</a> nahm sie 1841 wieder auf und verbreitete das ∂ weitreichend.<sup id="cite_ref-Aldrich_6-3" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-Aldrich-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></p> <div class="Vorlage_Zitat" style="margin:1em 40px;"> <div style="margin:1em 0;"> <blockquote style="margin:0;"> <p>„Sed quia uncorum accumulatio et legenti et scribenti molestior fieri solet, praetuli characteristica d differentialia vulgaria, differentialia autem partialia characteristica ∂ denotare.“</p> </blockquote> <blockquote style="margin:.5em 0 0 0;" lang="de-Latn"> <p>„Da jedoch die Anhäufung von Haken für das Lesen und Schreiben noch mühsamer ist, bevorzuge ich die üblichen d charakteristisch für gewöhnliche Differentiale, für partielle Differentiale ist charakteristisch ∂ angegeben.“</p> </blockquote> </div> <div class="cite" style="margin:-1em 0 1em 1em;"> – <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r181095833"><span class="Person h-card"><a href="https://de-m-wikipedia-org.translate.goog/wiki/Carl_Gustav_Jacob_Jacobi?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Carl Gustav Jacob Jacobi">Carl Gustav Jacob Jacobi</a></span>: <cite style="font-style:normal"><i>De determinantibus Functionalibus</i>, 1841<sup id="cite_ref-10" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></cite> </div> </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(3)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Anwendungen">Anwendungen</h2><span class="mw-editsection"> <a role="button" href="https://de-m-wikipedia-org.translate.goog/w/index.php?title=%E2%88%82&action=edit&section=3&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Abschnitt bearbeiten: Anwendungen" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>Bearbeiten</span> </a> </span> </div> <section class="mf-section-3 collapsible-block" id="mf-section-3"> <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 {\frac {\partial f}{\partial x}}={\frac {\partial f(x,y)}{\partial x}}={\frac {\partial }{\partial x}}f(x,y)}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal"> ∂ </mi> <mi> f </mi> </mrow> <mrow> <mi mathvariant="normal"> ∂ </mi> <mi> x </mi> </mrow> </mfrac> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal"> ∂ </mi> <mi> f </mi> <mo stretchy="false"> ( </mo> <mi> x </mi> <mo> , </mo> <mi> y </mi> <mo stretchy="false"> ) </mo> </mrow> <mrow> <mi mathvariant="normal"> ∂ </mi> <mi> x </mi> </mrow> </mfrac> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal"> ∂ </mi> <mrow> <mi mathvariant="normal"> ∂ </mi> <mi> x </mi> </mrow> </mfrac> </mrow> <mi> f </mi> <mo stretchy="false"> ( </mo> <mi> x </mi> <mo> , </mo> <mi> y </mi> <mo stretchy="false"> ) </mo> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\frac {\partial f}{\partial x}}={\frac {\partial f(x,y)}{\partial x}}={\frac {\partial }{\partial x}}f(x,y)} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/232fbc2c76fb1f2bbc6ce0ccee16bec34b8b95ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:28.533ex; height:5.843ex;" alt="{\displaystyle {\frac {\partial f}{\partial x}}={\frac {\partial f(x,y)}{\partial x}}={\frac {\partial }{\partial x}}f(x,y)}"> </noscript><span class="lazy-image-placeholder" style="width: 28.533ex;height: 5.843ex;vertical-align: -2.005ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/232fbc2c76fb1f2bbc6ce0ccee16bec34b8b95ad" data-alt="{\displaystyle {\frac {\partial f}{\partial x}}={\frac {\partial f(x,y)}{\partial x}}={\frac {\partial }{\partial x}}f(x,y)}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> ist die <i>partielle Ableitung von <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 f}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> f </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle f} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"> </noscript><span class="lazy-image-placeholder" style="width: 1.279ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" data-alt="{\displaystyle f}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> nach <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> <noscript> <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}"> </noscript><span class="lazy-image-placeholder" style="width: 1.33ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" data-alt="{\displaystyle x}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span></i>. Man braucht sie, wenn eine multivariable Funktion nach einer Variablen differenziert werden soll, um anzugeben, nach welcher.</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 {\frac {\partial \mathbf {f} }{\partial \mathbf {x} }}={\frac {\partial (f_{1},f_{2},\cdots ,f_{m})}{\partial (x_{1},x_{2},\cdots ,x_{n})}}={\begin{pmatrix}{\cfrac {\partial f_{1}}{\partial x_{1}}}&\cdots &{\cfrac {\partial f_{1}}{\partial x_{n}}}\\\vdots &\ddots &\vdots \\{\cfrac {\partial f_{m}}{\partial x_{1}}}&\cdots &{\cfrac {\partial f_{m}}{\partial x_{n}}}\end{pmatrix}}}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal"> ∂ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> f </mi> </mrow> </mrow> <mrow> <mi mathvariant="normal"> ∂ </mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold"> x </mi> </mrow> </mrow> </mfrac> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal"> ∂ </mi> <mo stretchy="false"> ( </mo> <msub> <mi> f </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <msub> <mi> f </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> <mo> , </mo> <mo> ⋯ </mo> <mo> , </mo> <msub> <mi> f </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> m </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> </mrow> <mrow> <mi mathvariant="normal"> ∂ </mi> <mo stretchy="false"> ( </mo> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 2 </mn> </mrow> </msub> <mo> , </mo> <mo> ⋯ </mo> <mo> , </mo> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> n </mi> </mrow> </msub> <mo stretchy="false"> ) </mo> </mrow> </mfrac> </mrow> <mo> = </mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo> ( </mo> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> ∂ </mi> <msub> <mi> f </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> ∂ </mi> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mtd> <mtd> <mo> ⋯ </mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> ∂ </mi> <msub> <mi> f </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> ∂ </mi> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> n </mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mo> ⋮ </mo> </mtd> <mtd> <mo> ⋱ </mo> </mtd> <mtd> <mo> ⋮ </mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> ∂ </mi> <msub> <mi> f </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> m </mi> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> ∂ </mi> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mn> 1 </mn> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mtd> <mtd> <mo> ⋯ </mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> ∂ </mi> <msub> <mi> f </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> m </mi> </mrow> </msub> </mrow> </mstyle> </mrow> <mrow> <mpadded width="0" height="8.6pt" depth="3pt"> <mrow></mrow> </mpadded> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal"> ∂ </mi> <msub> <mi> x </mi> <mrow class="MJX-TeXAtom-ORD"> <mi> n </mi> </mrow> </msub> </mrow> </mstyle> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle {\frac {\partial \mathbf {f} }{\partial \mathbf {x} }}={\frac {\partial (f_{1},f_{2},\cdots ,f_{m})}{\partial (x_{1},x_{2},\cdots ,x_{n})}}={\begin{pmatrix}{\cfrac {\partial f_{1}}{\partial x_{1}}}&\cdots &{\cfrac {\partial f_{1}}{\partial x_{n}}}\\\vdots &\ddots &\vdots \\{\cfrac {\partial f_{m}}{\partial x_{1}}}&\cdots &{\cfrac {\partial f_{m}}{\partial x_{n}}}\end{pmatrix}}} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b10778e606cf915d91bcdde7816789a5f97a5a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.838ex; width:49.633ex; height:18.843ex;" alt="{\displaystyle {\frac {\partial \mathbf {f} }{\partial \mathbf {x} }}={\frac {\partial (f_{1},f_{2},\cdots ,f_{m})}{\partial (x_{1},x_{2},\cdots ,x_{n})}}={\begin{pmatrix}{\cfrac {\partial f_{1}}{\partial x_{1}}}&\cdots &{\cfrac {\partial f_{1}}{\partial x_{n}}}\\\vdots &\ddots &\vdots \\{\cfrac {\partial f_{m}}{\partial x_{1}}}&\cdots &{\cfrac {\partial f_{m}}{\partial x_{n}}}\end{pmatrix}}}"> </noscript><span class="lazy-image-placeholder" style="width: 49.633ex;height: 18.843ex;vertical-align: -8.838ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b10778e606cf915d91bcdde7816789a5f97a5a2" data-alt="{\displaystyle {\frac {\partial \mathbf {f} }{\partial \mathbf {x} }}={\frac {\partial (f_{1},f_{2},\cdots ,f_{m})}{\partial (x_{1},x_{2},\cdots ,x_{n})}}={\begin{pmatrix}{\cfrac {\partial f_{1}}{\partial x_{1}}}&\cdots &{\cfrac {\partial f_{1}}{\partial x_{n}}}\\\vdots &\ddots &\vdots \\{\cfrac {\partial f_{m}}{\partial x_{1}}}&\cdots &{\cfrac {\partial f_{m}}{\partial x_{n}}}\end{pmatrix}}}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span><br> nennt man die m×n-<a href="https://de-m-wikipedia-org.translate.goog/wiki/Jacobimatrix?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Jacobimatrix">Jacobimatrix</a> von <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 f}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> f </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle f} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"> </noscript><span class="lazy-image-placeholder" style="width: 1.279ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" data-alt="{\displaystyle f}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> nach <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> <noscript> <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}"> </noscript><span class="lazy-image-placeholder" style="width: 1.33ex;height: 1.676ex;vertical-align: -0.338ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" data-alt="{\displaystyle x}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span> (Matrix der partiellen Ableitungen der von n Variablen abhängigen m-dimensionalen Funktion <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 f}"><semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi> f </mi> </mstyle> </mrow> <annotation encoding="application/x-tex"> {\displaystyle f} </annotation> </semantics> </math></span> <noscript> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"> </noscript><span class="lazy-image-placeholder" style="width: 1.279ex;height: 2.509ex;vertical-align: -0.671ex;" data-src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" data-alt="{\displaystyle f}" data-class="mwe-math-fallback-image-inline mw-invert skin-invert"> </span></span>).</p> <p>Neben partieller Ableitung, partiellem Differential und Jacobimatrix wird das ∂ auch in der <a href="https://de-m-wikipedia-org.translate.goog/wiki/Topologie_(Mathematik)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Topologie (Mathematik)">Topologie</a> als <a href="https://de-m-wikipedia-org.translate.goog/wiki/Rand_(Topologie)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Rand (Topologie)">Rand</a> einer <a href="https://de-m-wikipedia-org.translate.goog/wiki/Menge_(Mathematik)?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Menge (Mathematik)">Menge</a>, in der <a href="https://de-m-wikipedia-org.translate.goog/wiki/Homologische_Algebra?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Homologische Algebra">homologischen Algebra</a> als Grenzoperator in einem <a href="https://de-m-wikipedia-org.translate.goog/wiki/Kettenkomplex?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Kettenkomplex">Kettenkomplex</a> oder einer DG-Algebra und in der <a href="https://de-m-wikipedia-org.translate.goog/wiki/Dolbeault-Kohomologie?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Dolbeault-Kohomologie">Dolbeault-Kohomologie</a> als das <a href="https://de-m-wikipedia-org.translate.goog/wiki/Komplexe_Konjugation?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Komplexe Konjugation">komplex Konjugierte</a> des <a href="https://de-m-wikipedia-org.translate.goog/wiki/Wirtinger-Kalk%C3%BCl?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Dolbeault-Operator" title="Wirtinger-Kalkül">Dolbeault-Operators</a> über einer <a href="https://de-m-wikipedia-org.translate.goog/wiki/Komplexe_Differentialform?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Komplexe Differentialform">komplexen Differentialform</a> verwendet. In der <a href="https://de-m-wikipedia-org.translate.goog/wiki/Linguistik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="Linguistik">Linguistik</a> benutzt man das ∂ für <a href="https://de-m-wikipedia-org.translate.goog/wiki/Pr%C3%A4supposition?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Präsupposition">Präsuppositionen</a> eines Satzes.<sup id="cite_ref-11" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></p> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(4)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Kodierung">Kodierung</h2><span class="mw-editsection"> <a role="button" href="https://de-m-wikipedia-org.translate.goog/w/index.php?title=%E2%88%82&action=edit&section=4&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Abschnitt bearbeiten: Kodierung" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>Bearbeiten</span> </a> </span> </div> <section class="mf-section-4 collapsible-block" id="mf-section-4"> <table class="wikitable"> <caption> Kodierung in Unicode, <a href="https://de-m-wikipedia-org.translate.goog/wiki/HTML?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="HTML">HTML</a> und <a href="https://de-m-wikipedia-org.translate.goog/wiki/LaTeX?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="LaTeX">LaTeX</a> </caption> <tbody> <tr class="hintergrundfarbe6"> <th rowspan="2">Zeichen</th> <th colspan="2">Unicode</th> <th rowspan="2">Bezeichnung</th> <th colspan="3">HTML</th> <th rowspan="2">LaTeX<sup id="cite_ref-12" class="reference"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></th> </tr> <tr class="hintergrundfarbe6"> <th>Position</th> <th>Bezeichnung</th> <th>hexadezimal</th> <th>dezimal</th> <th>benannt</th> </tr> <tr style="text-align:center"> <td>∂</td> <td><code>U+2202</code></td> <td style="text-align:left"><span style="font-variant:small-caps;">partial differential</span></td> <td style="text-align:left">Partielles Differential</td> <td>&#x2202;</td> <td>&#8706;</td> <td>&part;</td> <td><code>\partial</code></td> </tr> <tr style="text-align:center"> <td>𝛛</td> <td><code>U+1D6DB</code></td> <td style="text-align:left"><span style="font-variant:small-caps;">mathematical bold partial differential</span></td> <td style="text-align:left">Mathematische fette partielle Ableitung</td> <td>&#x1D6DB;</td> <td>&#120539;</td> <td></td> <td><code>\mbfpartial</code></td> </tr> <tr style="text-align:center"> <td>𝜕</td> <td><code>U+1D715</code></td> <td style="text-align:left"><span style="font-variant:small-caps;">mathematical italic partial differential</span></td> <td style="text-align:left">Mathematische kursive partielle Ableitung</td> <td>&#x1D715;</td> <td>&#120597;</td> <td></td> <td><code>\mitpartial</code></td> </tr> <tr style="text-align:center"> <td>𝝏</td> <td><code>U+1D74F</code></td> <td style="text-align:left"><span style="font-variant:small-caps;">mathematical bold italic partial differential</span></td> <td style="text-align:left">Mathematische fettkursive partielle Ableitung</td> <td>&#x1D74F;</td> <td>&#120655;</td> <td></td> <td><code>\mbfitpartial</code></td> </tr> <tr style="text-align:center"> <td>𝞉</td> <td><code>U+1D789</code></td> <td style="text-align:left"><span style="font-variant:small-caps;">mathematical sans-serif bold partial differential</span></td> <td style="text-align:left">Mathematische serifenlose fette partielle Ableitung</td> <td>&#x1D789;</td> <td>&#120713;</td> <td></td> <td><code>\mbfsanspartial</code></td> </tr> <tr style="text-align:center"> <td>𝟃</td> <td><code>U+1D7C3</code></td> <td style="text-align:left"><span style="font-variant:small-caps;">mathematical sans-serif bold italic partial differential</span></td> <td style="text-align:left">Mathematische serifenlose fettkursive partielle Ableitung</td> <td>&#x1D7C3;</td> <td>&#120771;</td> <td></td> <td><code>\mbfitsanspartial</code></td> </tr> </tbody> </table> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(5)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Weblink">Weblink</h2><span class="mw-editsection"> <a role="button" href="https://de-m-wikipedia-org.translate.goog/w/index.php?title=%E2%88%82&action=edit&section=5&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Abschnitt bearbeiten: Weblink" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>Bearbeiten</span> </a> </span> </div> <section class="mf-section-5 collapsible-block" id="mf-section-5"> <div class="sisterproject" style="margin:0.1em 0 0 0;"> <span class="noviewer" style="display:inline-block; line-height:10px; min-width:1.6em; text-align:center;" aria-hidden="true" role="presentation"><span class="mw-default-size" typeof="mw:File"><span title="Wiktionary"> <noscript> <img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Wiktfavicon_en.svg/16px-Wiktfavicon_en.svg.png" decoding="async" width="16" height="16" class="mw-file-element" data-file-width="16" data-file-height="16"> </noscript><span class="lazy-image-placeholder" style="width: 16px;height: 16px;" data-src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Wiktfavicon_en.svg/16px-Wiktfavicon_en.svg.png" data-alt="" data-width="16" data-height="16" data-srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Wiktfavicon_en.svg/24px-Wiktfavicon_en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Wiktfavicon_en.svg/32px-Wiktfavicon_en.svg.png 2x" data-class="mw-file-element"> </span></span></span></span><b><a href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://de.wiktionary.org/wiki/del" class="extiw" title="wikt:del">Wiktionary: del</a></b> – Bedeutungserklärungen, Wortherkunft, Synonyme, Übersetzungen </div> </section> <div class="mw-heading mw-heading2 section-heading" onclick="mfTempOpenSection(6)"> <span class="indicator mf-icon mf-icon-expand mf-icon--small"></span> <h2 id="Quellen">Quellen</h2><span class="mw-editsection"> <a role="button" href="https://de-m-wikipedia-org.translate.goog/w/index.php?title=%E2%88%82&action=edit&section=6&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Abschnitt bearbeiten: Quellen" class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet "> <span class="minerva-icon minerva-icon--edit"></span> <span>Bearbeiten</span> </a> </span> </div> <section class="mf-section-6 collapsible-block" id="mf-section-6"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://www.compart.com/de/unicode/U%2B2202">Unicode-Zeichen „∂“ (U+2202)</a>, Daten zum Symbol</span></li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-2">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivative-and-gradient-articles/a/introduction-to-partial-derivatives">Introduction to partial derivatives</a>, <a href="https://de-m-wikipedia-org.translate.goog/wiki/Khan_Academy?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Khan Academy">Khan Academy</a></span></li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-3">↑</a></span> <span class="reference-text">Prof. Stefan Kooths, Nicole Wägner: <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://nanopdf.com/download/formel-bersicht_pdf">Formel-Übersicht</a>, Abschnitt Operatoren und Funktionen. <a href="https://de-m-wikipedia-org.translate.goog/wiki/University_of_Applied_Sciences_Europe?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="mw-redirect" title="University of Applied Sciences Europe">Business and Information Technology School</a>, 2014.</span></li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-4">↑</a></span> <span class="reference-text">Malcolm Pemberton, Nicholas Rau: <i><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://books.google.de/books?id%3DH92Z6yfhxk8C">Mathematics for Economists: An Introductory Textbook</a></i>. University of Toronto Press, 3. Ausgabe 2011. <a href="https://de-m-wikipedia-org.translate.goog/wiki/Spezial:ISBN-Suche/1442612762?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="internal mw-magiclink-isbn">ISBN 1442612762</a>. Zitat S, 270/271: <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://books.google.de/books?id%3DH92Z6yfhxk8C%26lpg%3DPA271%26pg%3DPA271%26redir_esc%3Dy%23v%3Donepage%26q%3Dpronounced%26f%3Dfalse">„pronounced 'partial-dee-eff-by-dee-ex'“.</a></span></li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-5">↑</a></span> <span class="reference-text">M. Y. Gokhale, N. S. Mujumdar, S. S. Kulkarni, A. N. Singh, K. R. Atal: <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://books.google.co.uk/books?id%3DCbIqX6TxJVMC%26pg%3DSA10-PA2%23v%3Donepage%26q%26f%3Dfalse">Engineering Mathematics-i</a>. Nirali Prakashan, 1981, Abschnitt 10.5. <a href="https://de-m-wikipedia-org.translate.goog/wiki/Spezial:ISBN-Suche/8190693549?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="internal mw-magiclink-isbn">ISBN 8190693549</a>. Zitat S. 10.2: „we read it as dabba z by dabba x (or del z by del x)“.</span></li> <li id="cite_note-Aldrich-6"><span class="mw-cite-backlink">↑ <sup><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-Aldrich_6-0">a</a></sup> <sup><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-Aldrich_6-1">b</a></sup> <sup><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-Aldrich_6-2">c</a></sup> <sup><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-Aldrich_6-3">d</a></sup></span> <span class="reference-text">John Aldrich: <a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=http://jeff560.tripod.com/calculus.html">Earliest Uses of Symbols of Calculus</a>, Abschnitt <i>partial derivative</i>. Website Jeff Millers, Quelle für gesamte Verwendungsgeschichte.</span></li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-7">↑</a></span> <span class="reference-text">Richard A. Silverman: <i><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://books.google.de/books?id%3DCQ-kqE9Yo9YC%26lpg%3DPA216%26pg%3DPA216%26redir_esc%3Dy%23v%3Donepage%26q%26f%3Dfalse">Essential Calculus with Applications</a></i>. Courier Corporation, 1977; zweite Ausgabe 1989, S. 216. Dover Publications Inc, New York. <a href="https://de-m-wikipedia-org.translate.goog/wiki/Spezial:ISBN-Suche/0486660974?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="internal mw-magiclink-isbn">ISBN 0486660974</a></span></li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-8">↑</a></span> <span class="reference-text"><a href="https://de-m-wikipedia-org.translate.goog/wiki/Marie_Jean_Antoine_Nicolas_Caritat,_Marquis_de_Condorcet?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Marie Jean Antoine Nicolas Caritat, Marquis de Condorcet">Marie Jean Antoine Nicolas Caritat, Marquis de Condorcet</a>: <i><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=http://visualiseur.bnf.fr/CadresFenetre?O%3DNUMM-3568%26I%3D323%26M%3Dpagination">Memoire sur les Equations aux différence partielles</a></i>. In: Histoire de L'Academie Royale des Sciences, Annee M. DCCLXXIII (1773). S. 151–178, Zitat S. 152.</span></li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-9">↑</a></span> <span class="reference-text"><a href="https://de-m-wikipedia-org.translate.goog/wiki/Adrien-Marie_Legendre?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Adrien-Marie Legendre">Adrien-Marie Legendre</a>: <i><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://gallica.bnf.fr/ark:/12148/bpt6k3585j/f95.image">Memoire sur la manière de distinguer les maxima des minima dans le Calcul des Variations</a></i>. In: Histoire de l'Academie Royale des Sciences, Annee M. DCCLXXXVI (1786), Paris, M. DCCXXXVIII (1788). S. 7–37, Zitat Fußnote S. 8.</span></li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-10">↑</a></span> <span class="reference-text"><a href="https://de-m-wikipedia-org.translate.goog/wiki/Carl_Gustav_Jacob_Jacobi?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Carl Gustav Jacob Jacobi">Carl Gustav Jacob Jacobi</a>: <i>De determinantibus Functionalibus</i>. In: <i><a href="https://de-m-wikipedia-org.translate.goog/wiki/Journal_f%C3%BCr_die_reine_und_angewandte_Mathematik?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Journal für die reine und angewandte Mathematik">Journal für die reine und angewandte Mathematik</a>.</i> Band 22, 1841, S. 319–352, S. 393–438 im 1. Band der gesammelten Werke.</span></li> <li id="cite_note-11"><span class="mw-cite-backlink"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-11">↑</a></span> <span class="reference-text">Ljudmila Geist, Björn Rothstein: <i><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://books.google.de/books?hl%3Dde%26id%3DIWzBRNdmD-EC%26q%3D%25E2%2588%2582%23v%3Dsnippet%26q%3D%25E2%2588%2582%26f%3Dfalse">Kopulaverben und Kopulasätze: Intersprachliche und intrasprachliche Aspekte</a></i>. Linguistische Arbeiten, Band 512. Hrsg. Walter de Gruyter, 2012, Erstausgabe 2007. Max Niemeyer Verlag, Tübingen. <a href="https://de-m-wikipedia-org.translate.goog/wiki/Spezial:ISBN-Suche/3110938839?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" class="internal mw-magiclink-isbn">ISBN 3110938839</a>. S. 154, Zitat: »„∂“ dient als Marker für Präsuppositionen«.</span></li> <li id="cite_note-12"><span class="mw-cite-backlink"><a href="https://de-m-wikipedia-org.translate.goog/wiki/%E2%88%82?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#cite_ref-12">↑</a></span> <span class="reference-text">Will Robertson: <style data-mw-deduplicate="TemplateStyles:r246413598">.mw-parser-output .webarchiv-memento{color:var(--color-base,#202122)!important}</style><a rel="nofollow" class="external text" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://web.archive.org/web/20200810023806/http://mirrors.ibiblio.org/CTAN/macros/latex/contrib/unicode-math/unimath-symbols.pdf">Symbols defined by unicode-math</a> (<a href="https://de-m-wikipedia-org.translate.goog/wiki/Web-Archivierung?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB#Begrifflichkeiten" title="Web-Archivierung"><span class="webarchiv-memento">Memento</span></a> vom 10. August 2020 im <i><a href="https://de-m-wikipedia-org.translate.goog/wiki/Internet_Archive?_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB" title="Internet Archive">Internet Archive</a></i>), 31. Januar 2020</span></li> </ol> </section> </div> <noscript> <img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=mobile" alt="" width="1" height="1" style="border: none; position: absolute;"> </noscript> <div class="printfooter" data-nosnippet=""> Abgerufen von „<a dir="ltr" href="https://translate.google.com/website?sl=auto&tl=en&hl=en-GB&u=https://de.wikipedia.org/w/index.php?title%3D%E2%88%82%26oldid%3D250602955">https://de.wikipedia.org/w/index.php?title=∂&oldid=250602955</a>“ </div> </div> </div> <div class="post-content" id="page-secondary-actions"> </div> </main> <footer class="mw-footer minerva-footer" role="contentinfo"><a class="last-modified-bar" href="https://de-m-wikipedia-org.translate.goog/w/index.php?title=%E2%88%82&action=history&_x_tr_sl=auto&_x_tr_tl=en&_x_tr_hl=en-GB"> <div class="post-content last-modified-bar__content"><span class="minerva-icon minerva-icon-size-medium minerva-icon--modified-history"></span> <span class="last-modified-bar__text modified-enhancement" data-user-name="Christian1985" data-user-gender="unknown" data-timestamp="1732353432"> <span>Zuletzt bearbeitet am 23. 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