       Re: Differentiate of Abs[x] ???

• To: mathgroup at smc.vnet.net
• Subject: [mg53087] Re: Differentiate of Abs[x] ???
• From: Peter Pein <petsie at arcor.de>
• Date: Thu, 23 Dec 2004 07:58:20 -0500 (EST)
• References: <cq0sv8\$2h8\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```idyllic wrote:
> Dear all,
>   If I have a complex-valued funciton Z=Z(x1,x2,y) where x1,x2,y are
> all real varables. Now I demand that |Z|^2 are local minimums at y=y1
> and y=y2 with some choices of x1 and x2. (where |...| denotes absolute
> value.)
>
>   My idea is that, I differentiate |Z|^2 w.r.t y, then subtitute y1
> and y2 into this equation and demand each equation 0; finally solve
> the two simultaneous equations.
>
>   But I found a big problem that Mathematica can't approach the
> differentiation of absolute values? Another question, is my
> method right? and is the differentiation of absolute value very hard
> to approach mathematically?
> Thanks for every ideas.           Sincerely
>
Try TagSet :

Unprotect[Derivative];
Derivative /: Derivative[Abs] := Sign;
Protect[Derivative];

In:=
D[Abs[Z[x1, x2, y]]^2, y]
Out=
2*Abs[Z[x1, x2, y]]*Sign[Z[x1, x2, y]]*Derivative[0, 0, 1][Z][x1, x2, y]

Peter

--
Peter Pein
Berlin

```

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