Question

If `f(x) = 4x -2` and `g(x) = e^(-x^3-1)`, what is `f'(g(x))`?

Answer 1

`12x^2e^(-x^3-1)=(12/e)x^2e^(-x^3)`.

Explanation:

`f(g(x)=4g(x)-1=4e^(-x^3-1)-2`

Use `(e^u)'=(e^u)u'`.

#f'(g(x)) =(4e^(-x^3-1)-2)'=4(e^(-x^3-1))'=4e^(-x^3-1)(-x^3-1)'=4e^(-x^3-1)(3x^2)=(12/e)x^2e^(-x^3)#