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Defining a derivative that distributes for a function

• To: mathgroup at smc.vnet.net
• Subject: [mg64222] Defining a derivative that distributes for a function
• From: Andres Corrada-Emmanuel <acorrada at physics.umass.edu>
• Date: Tue, 7 Feb 2006 03:35:48 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

I'm trying to define a derivative for a function that distributes:

D[f[expr_],x_] ^:= f[D[expr,x]]

This gives me:

D[f[x^2],x] = f[2x]

and

D[f[x^4],x] = f[4x^3]

But D[f[x^2] + f[x^4],x] = 2xf'[x^2] + 4x^3f'[x^4] instead of the
desired:

D[f[x^2] + f[x^4],x] = f[2x] + f[4x^3]. Why? And how do I get the desired behaviour.

--------------------------------------
Andres Corrada-Emmanuel
Lecturer in Physics
Physics Department
University of Massachusetts at Amherst
--------------------------------------

• Follow-Ups:
  • Re: Defining a derivative that distributes for a function
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>