1. The problem statement, all variables and given/known data If a is a natural number, prove by induction that y = [g(x)]^a => y' = a[g(x)]^(a-1) * g'(x) 2. Relevant equations Let a = 2 y' = (2)[g(x)]^(2-1) g(x) = 2g(x)g'(x) Let a = 3 y' = (3)[g(x)]^(3-1) g(x) = 3g(x)^2 * g'(x) Let k be any natural number a(k) = y' = ak[g(x)]^(ak-1) * g'(x) 3. The attempt at a solution What I did in the above equation was to substitute 2 and 3 (both natural numbers) as a, in order to prove that every natural number k is applicable. I'm not all too familiar with induction, but am I on the right track? Or am I completely off? How do I prove the power rule through induction?