If a is a natural number, prove by induction that
y = [g(x)]^a => y' = a[g(x)]^(a-1) * g'(x)
Let a = 2
y' = (2)[g(x)]^(2-1) 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)
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?