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## Homework Statement

If a is a natural number, prove by induction that

y = [g(x)]^a => y' = a[g(x)]^(a-1) * g'(x)

## Homework 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)

## 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?