Question

If `f(x) =-sqrt(3x-1)` and `g(x) = (x+3)^3`, what is `f'(g(x))`?

Answer 1

`f' (g(x)) =( -9(x+3)^2)/(2 sqrt(3(x+3)^3 -1)`

Explanation:

`f(x) = -sqrt(3x-1)` and `g(x)=(x+3)^3`

`f(g(x)) = -sqrt(3(g(x))-1)`

`f(g(x))= -sqrt(3(x+3)^3 -1)`

`f' (g(x)) = (-1)*(1/(2 sqrt(3(x+3)^3 -1)))*3*3(x+3)^2*1`

`f' (g(x)) =( -9(x+3)^2)/(2 sqrt(3(x+3)^3 -1)`