Suppose that I = (-a, a) for some a > 0. A function f : I

Question:

Suppose that I = (-a, a) for some a > 0. A function f : I → R is said to be even if and only if f(-x) = f(x) for all x ∊ I, and said to be odd if and only if f(-x) = - f(x) for all x ∊ I.
a) Prove that if f is odd and differentiable on f, then f' is even on I.
b) Prove that if f is even and differentiable on f, then f' is odd on f.