Re: Re: Derivatives of user-defined control-flow functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg51132] Re: [mg51096] Re: Derivatives of user-defined control-flow functions*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Tue, 5 Oct 2004 04:37:36 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On 4 Oct 2004, at 19:18, Maxim wrote: > Notice that while > Mathematica's rule for the differentiation of If can be handy, it is, > strictly speaking, not correct; for example: > > In[9]:= > D[If[x == 0, 0, Sin[x]^2/x], x] > > Out[9]= > If[x == 0, 0, (2*Sin[x]*Cos[x])/x - Sin[x]^2/x^2] > > while the correct value for the derivative at zero is 1. > > Maxim Rytin > m.r at inbox.ru > > One may also argue that you defined this function incorectly, at least if you were intending to differentiate it at 0. Since: Normal[Sin[x]^2/x + O[x]^2] x the "correct" definition should be If[x == 0, x, Sin[x]^2/x] in which case differentiation will give the right answer. Andrzej Kozlowski Chiba, Japan http://www.akikoz.net/~andrzej/ http://www.mimuw.edu.pl/~akoz/