# Replace rule with function? Derivatives don't evaluate

Say I have an expression (call it expr) involving a function, f[x]. I'd like to be able to evaluate that for a particular choice of f[x] without setting that choice for the whole session. I thought to do this using a replacement,

expr /. f[x_]->x^2


(where expr is some expression involving f[x] and I want to set f to x^2), but this doesn't work on derivatives, e.g., if expr contains f'[x] then it will stay as f'[x] rather than become 2x.

What's the best solution to this problem?

• Check FullForm[f'[x]] to understand why, and figure out the appropriate replacement rule. – István Zachar Jan 10 '14 at 18:45
• István - alright, I can see why it doesn't work, although I'm not sure how to construct a more general replacement rule. Still learning. Any hints? – Adam Jan 11 '14 at 0:08
• You can replace f by a pure function if you want things like derivatives to work. f->Function[x, x^2] – Rojo Jan 11 '14 at 0:41
• That's perfect!! That's the sort of simple solution I was hoping existed. If you write it as an answer I'll happily check it. If you or someone else wouldn't mind explaining, is there a reason to prefer either this solution or your Block solution? – Adam Jan 11 '14 at 2:14
• Adam you should ping with a @ the user you talk to. I hadn't seen this last comment of yours. Both work in this case, but the Block solution is slightly more general, and is the general solution for what you explicitly asked for: "evaluate something for a particular choice of some symbol without it affecting the whole session" – Rojo May 30 '14 at 19:04

Using Block seems more appropriate

Block[{f}, f[x_]:=x^2;
expr]


Some different solutions to have this topic as a generic one:

expr = D[f[x y], x] + f[x, y]

expr /. f -> (#^2 &)

2 x + x^2


or more verbose:

expr /. f -> Function[x, x^2]

2 x + x^2


This functionality is also included in my dChange implementation from Analogue for Maple's dchange:

dChange[
expr,
f[x, y] == x^2
]

• Thank you, this a nice solution! – Dr_Zaszuś Oct 17 '17 at 11:47