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Defining a derivative that distributes for a function


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
--------------------------------------


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