# Chain Rule of a functional to an exponential

1. Apr 9, 2014

### BreathingGloom

1. The problem statement, all variables and given/known data
Suppose f is differentiable on $\mathbb R$ and $\alpha$ is a real number. Let $G(x) = [f(x)]^a$

Find the expression for $G'(x)$

2. Relevant equations

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

3. The attempt at a solution

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

2. Apr 9, 2014

### BreathingGloom

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

3. Apr 9, 2014

### PeroK

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

4. Apr 9, 2014

### BreathingGloom

Much appreciated!