?

AP® Calculus AB-BC

Free Version

Upgrade subject to access all content

Difficult

Derivative of $\sin(2\cos(\sin(2x)))$

APCALC-UXBBGJ

What is the derivative of:

$$y=\sin { ( 2\cos { ( \sin { ( 2x ) } ) } ) },$$

...with respect to $x$?

A

$\cfrac{dx}{dy}=-4\cos { ( 2\cos { ( \sin { ( 2x ) } ) } )\cdot \sin { ( \sin { ( 2x ) } ) \cdot \cos { ( 2x ) } } } $

B

$\cfrac{dx}{dy}=\sin { ( 2\cos { ( \sin { ( x ) } ) } ) \cdot \tan { ( \sin { ( 2x ) } ) \cdot \cos { ( 2x ) } } } $

C

$\cfrac{dx}{dy}=4\cos { ( 2\sin { ( \sin { ( 2x ) } ) } ) +\sin { ( \sin { ( { x }^{ 2 } ) } ) \cdot \cos { ( 2x ) } } } $

D

$\cfrac{dx}{dy}=-2\tan { ( 2\cos { ( \cos { ( x ) } ) } ) } \cdot \sin { ( \sin { ( 2x ) } ) \cdot \cos { ( 2x ) } } $