Find $f ^ { \prime }$ in terms of $g ^ { \prime }$.
$f ( x ) = x ^ { 7 } g ( x )$
A) $f ^ { t } ( x ) = 7 x ^ { 6 } f ^ { \prime } ( x ) + x ^ { 7 } g ^ { \prime } ( x )$
B) $f ^ { t } ( x ) = 7 x ^ { 6 } g ^ { \prime } ( x )$
C) $f ^ { t } ( x ) = 7 x ^ { 6 } g ( x ) + 7 x ^ { 7 } g ^ { \prime } ( x )$
D) $f ^ { t } ( x ) = 7 x ^ { 6 } g ( x ) + x ^ { 7 } g ^ { \prime } ( x )$
E) $f ^ { t } ( x ) = 7 x ^ { 6 } + g ^ { \prime } ( x )$

Question

Quizplus · Accepted Answer

Use the product rule. We have $f(x) = x^7g(x)$, so $f'(x) = 7x^6g(x) + x^7g'(x)$. Therefore, the correct answer is D.

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