Question

If `f(x)= x^2-x` and `g(x) = x^( 1/3 )`, what is `f'(g(x))`?

Answer 1

`1/3x^(-1/3)(2-x^(-1/3))`

Explanation:

`f(g)=g^2-g=(x^(1/3))^2-x^(1/3)=x^(2/3)-x^(1/3)`

`f'(g(x)`

`= (x^(2/3)-x^(1/3))'`

`=2/3x^(-1/3)-1/3x^(-2/3)`

`=1/3x^(-1/3)(2-x^(-1/3))`