Re: Defining a derivative that distributes for a function
- To: mathgroup at smc.vnet.net
- Subject: [mg64243] Re: Defining a derivative that distributes for a function
- From: David Bailey <dave at Remove_Thisdbailey.co.uk>
- Date: Wed, 8 Feb 2006 03:53:30 -0500 (EST)
- References: <ds9mqp$48$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Andres Corrada-Emmanuel wrote: > 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 > -------------------------------------- > The built-in operation of D (and Integrate) can make it hard to add extensions like this. One solution is to define your own derivative operation - say DD - and define some recursive rules for that. One of those rules might make use of the built-in D to mop up all the usual stuff. David Bailey http://www.dbaileyconsultancy.co.uk