Find the Derivative of the Function $y ( x ) = 7 \cos \left( e ^ { x } \right) + 9 e ^ { x } \cos x$

Multiple Choice

Find the derivative of the function. $y ( x ) = 7 \cos \left( e ^ { x } \right) + 9 e ^ { x } \cos x$

A) $y' ( x ) = e ^ { x } \left( - 7 \sin \left( e ^ { x } \right) + 9 \cos x - 9 \sin x \right)$
B) $y' ( x ) = - 7 \sin \left( e ^ { x } \right) + 9 \sin x - 9 \cos x$
C) $y' ( x ) = - 7 \sin \left( e ^ { x } \right) + 9 \cos x - 9 \sin x$
D) $y '( x ) = e ^ { x } \left( - 7 \sin \left( e ^ { x } \right) - 9 \cos x + 9 \sin x \right)$
E) $y ^ { \prime } ( x ) = e ^ { x ^ { 2 } } \left( - 7 \sin \left( e ^ { x } \right) - 9 \cos x + 9 \sin x \right)$