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http://functions.wolfram.com/12.01.20.0003.01
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D[Abs[x], {x, \[Alpha]}] == Abs[x]/(x^\[Alpha] Gamma[2 - \[Alpha]])
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Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["x", ",", "\[Alpha]"]], "}"]]], RowBox[List["Abs", "[", "x", "]"]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["Abs", "[", "x", "]"]], SuperscriptBox["x", RowBox[List["-", "\[Alpha]"]]]]], RowBox[List["Gamma", "[", RowBox[List["2", "-", "\[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> ∂ </mo> <mi> α </mi> </msup> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> x </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> x </mi> <mi> α </mi> </msup> </mrow> </mfrac> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <mi> x </mi> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ⁢ </mo> <msup> <mi> x </mi> <mrow> <mo> - </mo> <mi> α </mi> </mrow> </msup> </mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> α </mi> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> x </ci> <degree> <ci> α </ci> </degree> </bvar> <apply> <abs /> <ci> x </ci> </apply> </apply> <apply> <times /> <apply> <abs /> <ci> x </ci> </apply> <apply> <power /> <ci> x </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> α </ci> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> α </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["x_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["Abs", "[", "x_", "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Abs", "[", "x", "]"]], " ", SuperscriptBox["x", RowBox[List["-", "\[Alpha]"]]]]], RowBox[List["Gamma", "[", RowBox[List["2", "-", "\[Alpha]"]], "]"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
