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How do you find the derivative of #y=e^((4x^3+5)^2)#?

1 Answer

Dec 20, 2016

#y' = 24x^2(4x^3+5)e^((4x^3+5)^2)#

Explanation:

If #y=e^(f(x))#, then #y'=f'(x)e^(f(x))#

In order to differentiate #f(x)#, we must use the chain rule, #[f(x)]^n=n[f(x)]^(n-1)f'(x)#

#f'(x)=2(4x^3+5)12x^2=24x^2(4x^3+5)#

So #y' = 24x^2(4x^3+5)e^((4x^3+5)^2)#

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