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 Quotient

 http://functions.wolfram.com/04.07.20.0002.01

 Input Form

 D[Quotient[x, n], x] == Sign[n] Sum[DiracDelta[x - k n], {k, -Infinity, Infinity}]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "x"], RowBox[List["Quotient", "[", RowBox[List["x", ",", " ", "n"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["Sign", "[", "n", "]"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List["DiracDelta", "[", RowBox[List["x", "-", RowBox[List["k", " ", "n"]]]], "]"]]]]]]]]]]

 MathML Form

 quotient ( x , n ) x sgn ( n ) k = - δ DiracDelta ( x - k n ) x quotient x n Sign n k -1 DiracDelta x -1 k n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["x_"]]], RowBox[List["Quotient", "[", RowBox[List["x_", ",", "n_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Sign", "[", "n", "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", RowBox[List["-", "\[Infinity]"]]]], "\[Infinity]"], RowBox[List["DiracDelta", "[", RowBox[List["x", "-", RowBox[List["k", " ", "n"]]]], "]"]]]]]]]]]]

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

 2001-10-29