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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