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http://functions.wolfram.com/12.01.13.0001.01
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Derivative[1][w][x] == UnitStep[x] - UnitStep[-x] /; w[x] == Abs[x]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "x", "]"]], "\[Equal]", RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], "-", RowBox[List["UnitStep", "[", RowBox[List["-", "x"]], "]"]]]]]], "/;", RowBox[List[RowBox[List["w", "[", "x", "]"]], "\[Equal]", RowBox[List["Abs", "[", "x", "]"]]]]]]]]
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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> <mrow> <mrow> <msup> <mi> w </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <semantics> <mi> θ </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <semantics> <mi> θ </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mo> - </mo> <mi> x </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <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> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> x </ci> </bvar> <apply> <ci> w </ci> <ci> x </ci> </apply> </apply> <apply> <plus /> <apply> <ci> UnitStep </ci> <ci> x </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> UnitStep </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> w </ci> <ci> x </ci> </apply> <apply> <abs /> <ci> x </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], "-", RowBox[List["UnitStep", "[", RowBox[List["-", "x"]], "]"]]]], "/;", RowBox[List[RowBox[List["w", "[", "x", "]"]], "\[Equal]", RowBox[List["Abs", "[", "x", "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
