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AP® Calculus AB-BC

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Moderate

Product Rule Challenge: Navigating $e^x$

APCALC-IZKFYF

What is the derivative of $y={ 5xe }^{ x }+{ 2x }^{ 2 }{ e }^{ x }{ -e }^{ x }$ with respect to $x$?

A

$\cfrac{dy}{dx}={ 4x }^{ 2 }{ e }^{ x }{ -9xe }^{ x }{ -e }^{ x }$

B

$\cfrac{dy}{dx}={ x }^{ 2 }{ e }^{ x }{ -9xe }^{ x }{ +4e }^{ x }$

C

$\cfrac{dy}{dx}={ 2x }^{ 2 }{ e }^{ x }{ +9xe }^{ x }{ +4e }^{ x }$

D

$\cfrac{dy}{dx}=4x^{ 2 }{ e }^{ x }{ +xe }^{ x }{ -4e }^{ x }$