Chain Rule of a functional to an exponential

[BreathingGloom]

Homework Statement

Suppose f is differentiable on $\mathbb R$ and $\alpha$ is a real number. Let $G(x) = [f(x)]^a$

Find the expression for $G'(x)$

Homework Equations

I'm pretty sure that I got this one right, but I really want to double check and make sure.

The Attempt at a Solution

$G'(x) = a[f(x)]^{a-1} \cdot f'(x)$

 

[BreathingGloom]

Functional to an exponential.. haha. Not exactly what I meant, but okay.

 

[PeroK]

That's correct. If you are being precise α ≠ 0.

 

[BreathingGloom]

Much appreciated!