Question

If `f(x)= sin3x` and `g(x) = 2x^2 -3x`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

`f'(g(x))*g'(x)=cos(6x^2-9x)*(12x-9)`

Explanation:

We have

`f(g(x))=sin(3(2x^2-3x))=sin(6x^2-9x)`
By the chain rule

`f'(g(x))*g'(x)` we get

`cos(6x^2-9x)*(12x-9)`