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 UnitStep

 http://functions.wolfram.com/14.01.20.0002.01

 Input Form

 D[UnitStep[x], x] == (UnitStep[x] + UnitStep[-x] - DiscreteDelta[x] - 1)/ (1 - DiscreteDelta[x]) /; x != 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["D", "[", RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], ",", "x"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], "+", RowBox[List["UnitStep", "[", RowBox[List["-", "x"]], "]"]], "-", RowBox[List["DiscreteDelta", "[", "x", "]"]], "-", "1"]], RowBox[List["1", "-", RowBox[List["DiscreteDelta", "[", "x", "]"]]]]]]], "/;", RowBox[List["x", "\[NotEqual]", "0"]]]]]]

 MathML Form

 θ UnitStep ( x ) x θ UnitStep ( x ) + θ UnitStep ( - x ) - δ DiscreteDelta ( x ) - 1 1 - δ DiscreteDelta ( x ) /; x 0 Condition x UnitStep x UnitStep x UnitStep -1 x -1 DiscreteDelta x -1 1 -1 DiscreteDelta x -1 x 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["x_"]]], RowBox[List["UnitStep", "[", "x_", "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["UnitStep", "[", "x", "]"]], "+", RowBox[List["UnitStep", "[", RowBox[List["-", "x"]], "]"]], "-", RowBox[List["DiscreteDelta", "[", "x", "]"]], "-", "1"]], RowBox[List["1", "-", RowBox[List["DiscreteDelta", "[", "x", "]"]]]]], "/;", RowBox[List["x", "\[NotEqual]", "0"]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2007-05-02