Having a delayed assignment of the form

Derivative[1][f][x_] := HoldForm[f[x]]

works. But if there is a delayed assignment for f as in

f[x_] := g[x]
Derivative[1][f][x_] := HoldForm[f[x]]

the error

SetDelayed::write: Tag Function in ((g^\[Prime])[#1]&)[x_] is Protected.

occurs. Why is f[x] evaluated despite HoldForm and how can I write a delayed assignment of this form?


1 Answer 1


The problem is that Derivative has a built-in definition that applies whenever f gets a DownValues. For example, suppose you define:

f[x_] := x^2

Then, f`, or in FullForm, Derivative[1][f] already has a definition:


2 #1 &

which, as you can see, is a pure function. So, trying to define:

Derivative[1][f][x_] := rhs

is equivalent to doing:

(2 #1 &)[x_] := rhs

and this is why you get an error, since it is not possible to define a definition for the protected symbol Function. If you want to overwrite the default derivative of a function, you need to use:

Derivative[1][f] = g;





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