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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/