Find $f ^ { \prime }$ in terms of $g ^ { \prime }$. $f ( x ) = [ g ( x ) ] ^ { 4 }$
A) $f ^ { \prime } ( x ) = 4 g ( x )$
B) $f ^ { \prime } ( x ) = 4 [ g ( x ) ] ^ { 3 } g ^ { \prime } ( x )$
C) $f ^ { \prime } ( x ) = 4 \left[ g ^ { \prime } ( x ) \right] ^ { 3 }$
D) $f ^ { \prime } ( x ) = 4 [ g x ] \left[ x g ^ { \prime } + g \right]$
E) $f ^ { \prime } ( x ) = 4 g ^ { \prime } ( x )$

Question

Quizplus · Accepted Answer

Using the chain rule, we have
$$ f'(x) = 4[g(x)]^3 \cdot g'(x) = 4[g'(x)]^3 $$

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

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