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Re: Re: Problem with the Derivative of a Arg-function



On 8 Jun 2004, at 13:48, Alex Klishko wrote:

> Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote in message
>
>> I suppose you mean -Re[x]+2*Pi*n. But of course for complex  x  Re[x]
> Yes, of course.
>
>> is not differentiable (as a function of the complex variable x !) so
>> Mathematica is quite right not to return -1.
>
> Yes, but Mathematica is not right to return another definite number.
>
>
Yes, but only when you use N. In such cases it performs numerical 
differentiation. In the case of Arg it looks like a bug, as Maxim has 
already pointed out. Note, however that:


N[D[ComplexExpand[Arg[E^((-I)*x)], {x}], x] /. x -> 1]

-1.*Derivative[1][Re][1.]


Andrzej


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