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

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<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> b </mi> </msup> <mo> &#8290; </mo> <mrow> <msub> <mi> log </mi> <mi> a </mi> </msub> <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> <mfrac> <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> b </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> b </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> b </ci> </apply> <apply> <log /> <logbase> <ci> a </ci> </logbase> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <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> b </ci> </apply> <apply> <power /> <apply> <ln /> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#945; </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29