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AP® Calculus AB-BC

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Moderate

Higher Order Derivatives: Using the Product Rule

APCALC-FN$OQA

If $f\left( x \right) ={ x }^{ 4 }{ e }^{ x }$, then $f^{ \prime \prime }\left( x \right) =$

A

$12{ x }^{ 2 }{ e }^{ x }$

B

${ x }^{ 4 }{ e }^{ x }+4{ x }^{ 3 }{ e }^{ x }$

C

${ x }^{ 4 }{ e }^{ x }+4{ x }^{ 3 }{ e }^{ x }+12{ x }^{ 2 }{ e }^{ x }$

D

${ x }^{ 4 }{ e }^{ x }+8{ x }^{ 3 }{ e }^{ x }+12{ x }^{ 2 }{ e }^{ x }$