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[1][Abs] := Sign; Protect[Derivative]; In[3]:= D[Abs[Z[x1, x2, y]]^2, y] Out[3]= 2*Abs[Z[x1, x2, y]]*Sign[Z[x1, x2, y]]*Derivative[0, 0, 1][Z][x1, x2, y] Peter -- Peter Pein Berlin

**Follow-Ups**:**Re: Re: Differentiate of Abs[x] ???***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>