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

We use the chain rule: $$\frac { d } { d x } [ g ( x ) ] ^ { 4 } = 4 [ g ( x ) ] ^ { 3 } g ^ { \prime } ( x )$$ so the correct choice is (B).

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