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

*To*: mathgroup at smc.vnet.net*Subject*: [mg48556] Re: [mg48514] Re: Problem with the Derivative of a Arg-function*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sat, 5 Jun 2004 07:18:56 -0400 (EDT)*References*: <200406040849.EAA23630@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 4 Jun 2004, at 17:49, Alex Klishko wrote: >> On 2 Jun 2004, at 17:21, Andrzej Kozlowski wrote: >> >> I am not sure what you mean by "fase"? Is that just Arg[E^(-I*x)]? Are >> you saying that this is -Re[x] for all complex x? Well, that certianly >> is not true, even for real ones! > > You are right, Arg[E^(-I*x)] is equal to -x +2*Pi*n, where n is an > integer number so, that -Pi<%<Pi. I suppose you mean -Re[x]+2*Pi*n. But of course for complex x Re[x] is not differentiable (as a function of the complex variable x !) so Mathematica is quite right not to return -1. Of course D[ComplexExpand[Arg[E^((-I)*x)], {x}],Re[x]]//Simplify -1 but that is a completely differnt thing! Andrzej Kozlowski > > But I need an Arg's derivative. > As 2*Pi*n is the constant so the derivative doesn't depend on it. > So the derivative must be -1. > > By the way, > f[x_] = ComplexExpand[Arg[E^(-I*x)]]; N[D[f[x], x]] /. x -> x0 > > gives -1, for any x0 (if you substitute instead x0 any real number) >

**References**:**Re: Problem with the Derivative of a Arg-function***From:*klishko@mail.ru (Alex Klishko)