Find the Derivative Of $f ( x ) = \cos ^ { 2 } \left( \tan ^ { - 1 } x \right)$

Multiple Choice

Find the derivative of $f ( x ) = \cos ^ { 2 } \left( \tan ^ { - 1 } x \right)$

A) $\frac { \cos 2 \left( \tan ^ { - 1 } x \right) } { 1 + x ^ { 2 } }$
B) $\frac { 2 \cos \left( \tan ^ { - 1 } x \right) } { 1 + x ^ { 2 } }$
C) $\frac { - \sin 2 \left( \tan ^ { - 1 } x \right) } { 1 + x ^ { 2 } }$
D) $\frac { 2 \sin \left( \tan ^ { - 1 } x \right) } { 1 + x ^ { 2 } }$