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

Question

1519 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-30T12:45:31

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

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

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

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

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