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Differentiate of Abs[x] ???

• To: mathgroup at smc.vnet.net
• Subject: [mg52958] Differentiate of Abs[x] ???
• From: idyllic.math at gmail.com (idyllic)
• Date: Sat, 18 Dec 2004 03:59:31 -0500 (EST)
• 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
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