Rule calculus.differentiation.quotient

Parameters
Buggy	no
Rewrite rule	yes
Siblings

Rewrite rule

D(a) (b/c)   ⇒   ((c·(D(a) b))-(b·(D(a) c)))/(c^2)
D(a) (-(b/c))   ⇒   ((c·(D(a) (-b)))-((-b)·(D(a) c)))/(c^2)

Formal Mathematical Properties

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$1"/><OMV name="$2"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="calculus1" name="diff"/><OMBIND><OMS cd="fns1" name="lambda"/><OMBVAR><OMV name="$0"/></OMBVAR><OMA><OMS cd="arith1" name="divide"/><OMV name="$1"/><OMV name="$2"/></OMA></OMBIND></OMA><OMA><OMS cd="arith1" name="divide"/><OMA><OMS cd="arith1" name="minus"/><OMA><OMS cd="arith1" name="times"/><OMV name="$2"/><OMA><OMS cd="calculus1" name="diff"/><OMBIND><OMS cd="fns1" name="lambda"/><OMBVAR><OMV name="$0"/></OMBVAR><OMV name="$1"/></OMBIND></OMA></OMA><OMA><OMS cd="arith1" name="times"/><OMV name="$1"/><OMA><OMS cd="calculus1" name="diff"/><OMBIND><OMS cd="fns1" name="lambda"/><OMBVAR><OMV name="$0"/></OMBVAR><OMV name="$2"/></OMBIND></OMA></OMA></OMA><OMA><OMS cd="arith1" name="power"/><OMV name="$2"/><OMI>2</OMI></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$1"/><OMV name="$2"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="calculus1" name="diff"/><OMBIND><OMS cd="fns1" name="lambda"/><OMBVAR><OMV name="$0"/></OMBVAR><OMA><OMS cd="arith1" name="unary_minus"/><OMA><OMS cd="arith1" name="divide"/><OMV name="$1"/><OMV name="$2"/></OMA></OMA></OMBIND></OMA><OMA><OMS cd="arith1" name="divide"/><OMA><OMS cd="arith1" name="minus"/><OMA><OMS cd="arith1" name="times"/><OMV name="$2"/><OMA><OMS cd="calculus1" name="diff"/><OMBIND><OMS cd="fns1" name="lambda"/><OMBVAR><OMV name="$0"/></OMBVAR><OMA><OMS cd="arith1" name="unary_minus"/><OMV name="$1"/></OMA></OMBIND></OMA></OMA><OMA><OMS cd="arith1" name="times"/><OMA><OMS cd="arith1" name="unary_minus"/><OMV name="$1"/></OMA><OMA><OMS cd="calculus1" name="diff"/><OMBIND><OMS cd="fns1" name="lambda"/><OMBVAR><OMV name="$0"/></OMBVAR><OMV name="$2"/></OMBIND></OMA></OMA></OMA><OMA><OMS cd="arith1" name="power"/><OMV name="$2"/><OMI>2</OMI></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>