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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Differentiation > Symbolic differentiation > With respect to a





http://functions.wolfram.com/01.02.20.0013.02









  


  








Input Form





D[z^a, {a, n}] == z^a Log[z]^n /; Element[n, Integers] && n >= 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["a", ",", "n"]], "}"]]], SuperscriptBox["z", "a"]]], "\[Equal]", RowBox[List[SuperscriptBox["z", "a"], " ", SuperscriptBox[RowBox[List["Log", "[", "z", "]"]], "n"]]]]], " ", "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mi> n </mi> </msup> <msup> <mi> z </mi> <mi> a </mi> </msup> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> a </mi> <mi> n </mi> </msup> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <msup> <mi> z </mi> <mi> a </mi> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mi> n </mi> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> a </ci> <degree> <ci> n </ci> </degree> </bvar> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <apply> <power /> <apply> <ln /> <ci> z </ci> </apply> <ci> n </ci> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["a_", ",", "n_"]], "}"]]]]], SuperscriptBox["z_", "a_"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["z", "a"], " ", SuperscriptBox[RowBox[List["Log", "[", "z", "]"]], "n"]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29