       Re: Real/Comlex function problem with D

• To: mathgroup at smc.vnet.net
• Subject: [mg74226] Re: Real/Comlex function problem with D
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 15 Mar 2007 04:54:45 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <et8e29\$pqb\$1@smc.vnet.net>

```bar at ANTYSPAM.ap.krakow.pl wrote:
> Hi,
> I have a complex function F[x]
> When i defined:
> ff[x_]:=Arg[F[x]]   (* i tried ComplexExpand[Arg[F[x]]] too *)
>
> I obtainned good Plot[ff[x]] - its real - (no complex)
>
> When i try
> ff1[x_]:=D[ff[x],x];
>  I found ff1 is Complex funtion again !!
>
> Why ?
>
> (i tried Evaluate; Element[x,Reals]; FullSimplify - always the same)
>
> Regards, Olaf
>
>

Hi Olaf,

You might get better results by using ArcTan rather than Arg since
Mathematica does not know how to differentiate Arg. (Note that ArcTan
returns values between -Pi/2 and Pi/2, whereas Arg returns values
between -Pi and Pi.) Compare

In:=
ff[x_] := Arg[F[x]]
ff1[x_] := D[ff[x], x]
ff1[x]

Out=
Arg'[F[x]] F'[x]

with

In:=
ff[x_] := ArcTan[F[x]]
ff1[x_] := D[ff[x], x]
ff1[x]

Out=
F'[x]
---------
2
1 + F[x]

Regards,
Jean-Marc

```

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