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Re: substitution of functions in derivatives

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3415] Re: [mg3384] substitution of functions in derivatives
  • From: Allan Hayes <hay at haystack.demon.co.uk>
  • Date: Wed, 6 Mar 1996 01:45:26 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

pyl at ccr.jussieu.fr (lagre)
in [mg3384] substitution of functions in derivatives

raises the following problem (slightly simplified)

	f=u[x,y];
	df=D[f,x];
	df/.u[x_,y_]->Cos[x y]
	
 	 (1,0)
	u     [x, y]
	Not the expected -(y*Sin[x*y])

One solution is
	df/.u->(Cos[#1 #2]&)
	
	-(y Sin[x y])

Explanation:
	FullForm[df]
	
	Times[a, Derivative[1, 0][u][x, y]]

does not contain u[x_,y_].

* We must replace u with a two place function (x,y) --> Cos[x,y] *

Here are four other way of doing this
	df/.u->Function[{x,y}, Cos[x y]]

	v[x_,y_] := Cos[x y]
	df/.u->v

	df/.(v[x_,y_] := Cos[x y];u->v)

	df/.(u -> (v[x_,y_] := Cos[x y];v))
	
Allan Hayes
hay at haystack.demon.co.uk



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