D[HeavisideTheta[x], x] == DiracDelta[x]

Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "x"], RowBox[List["HeavisideTheta", "[", "x", "]"]]]], "\[Equal]", RowBox[List["DiracDelta", "[", "x", "]"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> HeavisideTheta </ci> </annotation-xml> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> x </mi> </mrow> </mfrac> <mo> &#63449; </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> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> x </ci> </bvar> <apply> <ci> HeavisideTheta </ci> <ci> x </ci> </apply> </apply> <apply> <ci> DiracDelta </ci> <ci> x </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["x_"]]], RowBox[List["HeavisideTheta", "[", "x_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["DiracDelta", "[", "x", "]"]]]]]]

2007-05-02