       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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```

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