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Re: D[myFunc[g[x]]] -> myFunc[D[g[x],x]: How to do in ch

• To: mathgroup at yoda.physics.unc.edu
• Subject: Re: D[myFunc[g[x]]] -> myFunc[D[g[x],x]: How to do in ch
• From: sfeir at mines.u-nancy.fr
• Date: Tue, 15 Sep 92 11:54:41 +0200

>(* Hi mathgroup,
>
>I hope you can help with this problem.  I want to give the function 'myFunc' 
>the property of being 'transparent' to differentiation.
>i.e., I want to have 
>
>  d myFunc[g[x]]                       d g[x]
>  --------------    give me    myFunc[ ------ ]                (1)
>	dx                               dx
>
>where g is an arbitrary function.  "Easy" I hear you say, just write...
>*)
I would suggest the following solution to your problem using tagged set
delayed

D[MyFunc[a_],b_]^:=MyFunc[D[a,b]]

TAGGED means the rule is associated with MyFunc and NOT with D
SET-DELAYED because the rule is executed when it is used and NOT when it is
defined.

EXAMPLES

D[MyFunc[x^n],x]
returns    MyFunc[n*x^(-1 + n)]

D[Sin[x^n],x]
returns    n*x^(-1 + n)*Cos[x^n]

there is no need to deprotect D

A.A. SFEIR
ECOLE DES MINES DE NANCY, FRANCE
sfeir at mines.u-nancy.fr