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variants of this functions
Log




Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Differentiation > Fractional integro-differentiation





http://functions.wolfram.com/01.04.20.0011.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "\[Alpha]"]], "}"]]], RowBox[List["(", RowBox[List[SuperscriptBox["z", "a"], " ", RowBox[List["Log", "[", "z", "]"]]]], ")"]]]], "\[Equal]", RowBox[List[RowBox[List["FDLogConstant", "[", 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> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mi> a </mi> </msup> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </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> log </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> <times /> <apply> <power /> <ci> z </ci> <ci> a </ci> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> &#8497;&#119966; </ci> <ci> log </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]_"]], "}"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["z_", "a_"], " ", RowBox[List["Log", "[", "z_", "]"]]]], ")"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["FDLogConstant", "[", RowBox[List["z", ",", "a", ",", "\[Alpha]"]], "]"]], " ", SuperscriptBox["z", RowBox[List["a", "-", "\[Alpha]"]]]]]]]]]


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





2001-10-29