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AP® Calculus AB-BC

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Chain Rule: Exponential to a Polynomial Power

APCALC-EWJGUS

What is the derivative of $ y=e^{2x^{^{2}}+1},$ with respect to ‘$x$’?

A

$\cfrac { dy }{ dx }={ xe }^{ { 4x }^{ 2 }+1 }$

B

$\cfrac { dy }{ dx }={ 8xe }^{ { x }^{ 2 }+1 }$

C

$\cfrac { dy }{ dx }={ 4xe }^{ { 2x }^{ 2 }+1 }$

D

$\cfrac { dy }{ dx }=-4xe^{ 2x^{ 4 }+1 }$

E

$\cfrac { dy }{ dx }=2xe^{ 2x+1 }$