Re: Problem with the Derivative of a Arg-function

• To: mathgroup at smc.vnet.net
• Subject: [mg48514] Re: Problem with the Derivative of a Arg-function
• From: klishko at mail.ru (Alex Klishko)
• Date: Fri, 4 Jun 2004 04:49:30 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```> 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.

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)

```

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