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) $\cos \left( g ^ { \prime } ( x ) \right)$

Question

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) $\cos \left( g ^ { \prime } ( x ) \right)$

Quizplus · Accepted Answer

The derivative of $F(x) = \sin(g(x))$ is found using the chain rule. The derivative of the outer function, $\sin(u)$, with respect to $u$ is $\cos(u)$, and the derivative of the inner function, $g(x)$, with respect to $x$ is $g'(x)$. Thus, $F'(x) = g'(x) \cos(g(x))$.

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

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