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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/01.02.20.0016.01









  


  








Input Form





D[z^a, {z, \[Alpha]}] == FDPowerConstant[z, a, \[Alpha]] z^(a - \[Alpha])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "\[Alpha]"]], "}"]]], SuperscriptBox["z", "a"]]], "\[Equal]", RowBox[List[RowBox[List["FDPowerConstant", "[", RowBox[List["z", ",", "a", ",", "\[Alpha]"]], "]"]], SuperscriptBox["z", RowBox[List["a", "-", "\[Alpha]"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mi> &#945; </mi> </msup> <msup> <mi> z </mi> <mi> a </mi> </msup> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mi> &#945; </mi> </msup> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mrow> <msubsup> <mi> &#8497;&#119966; </mi> <mi> exp </mi> <mrow> <mo> ( </mo> <mi> &#945; </mi> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mi> z </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> a </mi> <mo> - </mo> <mi> &#945; </mi> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <ci> &#945; </ci> </degree> </bvar> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#8497;&#119966; </ci> <ci> exp </ci> </apply> <ci> &#945; </ci> </apply> <ci> z </ci> <ci> a </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> </apply> </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["z_", ",", "\[Alpha]_"]], "}"]]]]], SuperscriptBox["z_", "a_"]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["FDPowerConstant", "[", RowBox[List["z", ",", "a", ",", "\[Alpha]"]], "]"]], " ", SuperscriptBox["z", RowBox[List["a", "-", "\[Alpha]"]]]]]]]]]


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





2001-10-29