Find the Derivative of the Function $w ( x ) = 2 \sec ( x ) \cdot \tan \left( x ^ { 2 } - 2 \right)$

Multiple Choice

Find the derivative of the function. $w ( x ) = 2 \sec ( x ) \cdot \tan \left( x ^ { 2 } - 2 \right)$

A) $w ^ { \prime } ( x ) = 2 \sec ^ { 2 } x \cdot \sin x \cdot \tan \left( x ^ { 2 } - 2 \right) + 4 x \cdot \sec x \cdot \sec ^ { 2 } \left( x ^ { 2 } - 2 \right)$
B) $w ^ { \prime } ( x ) = 2 \sec ^ { 2 } x \cdot \sin x \cdot \tan \left( x ^ { 2 } - 2 \right) + 4 x \cdot \sec x \cdot \sec ^ { 2 } ( 2 x - 2 )$
C) $w ^ { \prime } ( x ) = 2 \sec ^ { 2 } x \cdot \sin x \cdot \tan \left( x ^ { 2 } + 2 \right) + 4 x \cdot \sec x \cdot \sec ^ { 2 } ( 2 x - 2 )$
D) $w ^ { \prime } ( x ) = 2 \sec ^ { 2 } x \cdot \sin x \cdot \tan \left( x ^ { 2 } - 2 \right)$
E) $w ^ { \prime } ( x ) = 2 \sec ^ { 2 } x \cdot \sin x \cdot \tan \left( x ^ { 2 } - 2 \right) + 4 x \cdot \sec x \cdot \sec ^ { 2 } \left( x ^ { 2 } - 4 \right)$