Find the derivative of $g ( x ) = \cos ( \sin ( 2 x ) )$ .
A) $- 2 \cos ( 2 x ) \sin ( \sin ( 2 x ) )$
B) $2 \cos ( 2 x ) \sin ( \sin ( 2 x ) )$
C) $- 2 \sin ( \sin ( 2 x ) )$
D) $4 \sin ( \sin ( 2 x ) )$

Question

Quizplus · Accepted Answer

To find the derivative of $g(x) = \cos(\sin(2x))$, we use the chain rule. First, differentiate the outer function with respect to the inner function, $\frac{d}{d(\sin(2x))}(\cos(\sin(2x))) = -\sin(\sin(2x))$. Then, differentiate the inner function $\sin(2x)$ with respect to $x$, which gives $2\cos(2x)$. Multiply these derivatives together to get $-2\cos(2x)\sin(\sin(2x))$.

Find the Derivative Of g(x)=cos⁡(sin⁡(2x))g ( x ) = \cos ( \sin ( 2 x ) )g(x)=cos(sin(2x))

Find the Derivative Of $g ( x ) = \cos ( \sin ( 2 x ) )$