If $f ( x ) = 6 \cos x + \sin ^ { 2 } x$

Multiple Choice

If $f ( x ) = 6 \cos x + \sin ^ { 2 } x$ , find $f ^ { \prime } ( x )$ and $f ^ { \prime \prime } ( x )$

A) $f ^ { \prime \prime } ( x ) = - 6 \cos ( 2 x ) + 2 \cos ( x )$
B) $f ^ { \prime } ( x ) = - 6 \sin ( x ) + \sin ( 2 x )$
C) $f ^ { \prime } ( x ) = - 6 \sin ( 2 x ) + \sin ( x )$
D) $f ^ { \prime \prime } ( x ) = - 6 \cos ( x ) + 2 \cos ( 2 x )$
E) $f ^ { \prime \prime } ( x ) = - 2 \cos ( 2 x ) + 6 \cos ( x )$