Question

If `f(x) = x^2-4` and `g` is a differentiable function of `x`, what is the derivative of `f(g(x))`?

Answer 1

`[f(g(x))]'=2g(x)g'(x)`

Explanation:

`f(x)=x^2-4`

By Power Rule,

`f'(x)=2x`

So, by Chain Rule

`[f(g(x))]'=f'(g(x))cdot g'(x)=2g(x)g'(x)`

I hope that this was clear.