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

Question

Quizplus · Accepted Answer

Using the product rule, we have
$$f'(x)=7x^6g(x)+x^7g'(x)$$

Find f′f ^ { \prime }f′ In Terms Of g′g ^ { \prime }g′

Find $f ^ { \prime }$ In Terms Of $g ^ { \prime }$