Let $f ( x ) = \sin ^ { - 1 } ( \cos x )$

Multiple Choice

Let $f ( x ) = \sin ^ { - 1 } ( \cos x )$ on the interval $( 0 , \pi )$ Then $f ^ { \prime } ( x )$ is

A) -1
B) $\frac { - \sin x } { 1 + \cos ^ { 2 } x }$
C) $- \frac { \sin x } { \sqrt { 1 + \cos ^ { 2 } x } }$
D) 1
E) $\frac { \sin x } { \sqrt { 1 + \cos ^ { 2 } x } }$