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

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Answer 1 · 2016-12-20T17:34:23

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

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

How do you find the derivative of y=e^((4x^3+5)^2)y=e(4x3+5)2y=e^((4x^3+5)^2)?