Recall that a function f is called even if f(-x) = f(x) for all in its domain

Question:

Recall that a function f is called even if f(-x) = f(x) for all in its domain and odd if f(-x) = -f(x) for all such x. Prove each of the following.
(a) The derivative of an even function is an odd function.
(b) The derivative of an odd function is an even function.