Question

If `f(x)= sin3x` and `g(x) = 2x^2`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

`[f(g(x))]'=12x cos(6x^2)`

Explanation:

`f(g(x))=sin(3(2x^2) )= sin(6x^2)`

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

`=cos(6x^2)*12x`

`=12x cos(6x^2)`