Let f be a function. Then f is odd if f(-x) = -f(x) for all x in the domain of f.

hello your question is incomplete attached below is the complete question

f'(x) = -f'(-x)

Step-by-step explanation:

suppose f is differentiable even function

we will apply the definition of even function considering that f is differentiable

attached below is a detailed solution and from the solution it can be concluded that f' is odd everywhere in its domain, whenever f is even