** Final Answer

$\frac{d}{dx}\left(e^{\frac{1}{2}\left(x^3+4\right)}\right)$

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**** Step-by-step Solution **

Problem to solve:

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1

Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(e^{\frac{1}{2}\left(x^3+4\right)}\right)$

** Final Answer

$\frac{d}{dx}\left(e^{\frac{1}{2}\left(x^3+4\right)}\right)$