Find the Derivative of the Function and Simplify Your Answer $y = \cos ^ { 2 } x$

Multiple Choice

Find the derivative of the function and simplify your answer by using the trigonometric identities $y = \cos ^ { 2 } x$

A) $- 2 \cos ^ { 2 } x \sin ^ { 2 } x = 2 \sin 2 x$
B) $2 \cos x \sin x = \sin 2 x$
C) $- 2 \cos x \sin x = - \sin 2 x$
D) $2 \cos ^ { 2 } x \sin x = 2 \sin x$
E) $2 \cos ^ { 2 } x \sin ^ { 2 } x = 2 \sin 2 x$