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)#