Let $F ( x ) = \sin ( g ( x ) )$

Let $F ( x ) = \sin ( g ( x ) )$ where g is differentiable. Find $F ^ { \prime } ( x )$

A) $g ( x ) \cos x$
B) $- g ( x ) \sin x$
C) $- g ^ { \prime } ( x ) \sin x$
D) $g ^ { \prime } ( x ) \cos x$
E) $g ^ { \prime } ( x ) \cos ( g ( x ) )$
F) $g ^ { \prime } ( x ) \sin ( g ( x ) )$
G) $\cos ( g ( x ) )$
H) $\cos \left( g ^ { \prime } ( x ) \right)$

Correct Answer:

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