Question

If `f(x)= 3x^3-2` and `g(x) = e^(2x`, what is `f'(g(x))`?

Answer 1

`f'(g(x))=9e^(4x)`

Explanation:

`f(x)=3x^3-2`

By Power Rule,

`f'(x)=9x^2`

So, since `g(x)=e^(2x)`

`f'(g(x))=f'(e^(2x))=9(e^(2x))^2=9e^(4x)`

I hope that this was clear.