How do you find the derivative of $e^(-5x^3+x)$ ?

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Answer 1 · 2018-03-14T15:13:19

$-15e^(-5x^3+x)x^2+e^(-5x^3+x)$

According to the chain rule, $(f(g(x)))'=f'(g(x))*g'(x)$

Here, we have:

$f(u)=e^u$ , where

$u=g(x)=-5x^3+x$

We do:

$d/(du)e^u*(-(d/dx5x^3-d/dxx))$

$e^u*(-(15x^2-1))$

$e^u(-15x^2+1)$

$-15e^ux^2+e^u$

But since $u=-5x^3+x$ , we say:

$-15e^(-5x^3+x)x^2+e^(-5x^3+x)$

How do you find the derivative of e^(-5x^3+x)e^(-5x^3+x)?