D[UnitStep[x], x] == DiracDelta[x] /; x != 0

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "x"], RowBox[List["UnitStep", "[", "x", "]"]]]], "\[Equal]", RowBox[List["DiracDelta", "[", "x", "]"]]]], "/;", RowBox[List["x", "\[NotEqual]", "0"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> x </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <semantics> <mi> &#948; </mi> <annotation-xml encoding='MathML-Content'> <ci> DiracDelta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> &#8800; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> x </ci> </bvar> <apply> <ci> UnitStep </ci> <ci> x </ci> </apply> </apply> <apply> <ci> DiracDelta </ci> <ci> x </ci> </apply> </apply> <apply> <neq /> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["x_"]]], RowBox[List["UnitStep", "[", "x_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["DiracDelta", "[", "x", "]"]], "/;", RowBox[List["x", "\[NotEqual]", "0"]]]]]]]]

2001-10-29