Q24Short answer
A function f : R → R satisfies the equation f ( x + y) = f (x) f (y) for all x, y ∈ R, f (x) ≠ 0. Suppose that the function is differentiable at x = 0 and f ′ (0) = 2. Prove that f ′(x) = 2 f (x). Differentiate each of the following w.r.t. x (Exercises 25 to 43) :