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: <email@example.com>
- Sender: owner-wri-mathgroup at wolfram.com
> 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
> 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 :
Derivative /: Derivative[Abs] := Sign;
D[Abs[Z[x1, x2, y]]^2, y]
2*Abs[Z[x1, x2, y]]*Sign[Z[x1, x2, y]]*Derivative[0, 0, 1][Z][x1, x2, y]
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