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

Question:

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