Find the Derivatives of the Following Functions:
(A) $f ( x ) = \sin ^ { - 1 } \left( x ^ { 2 } \right)$

Essay

Find the derivatives of the following functions:
(a) $f ( x ) = \sin ^ { - 1 } \left( x ^ { 2 } \right)$ (b) $f ( x ) = \left( \sin ^ { - 1 } x \right) ^ { 2 }$ (c) $f ( x ) = x \sin ^ { - 1 } \left( x ^ { 3 } \right)$ (d) $f ( x ) = \tan ^ { - 1 } \left( \frac { x + 1 } { x - 1 } \right)$ (e) $f ( x ) = \cos ^ { - 1 } \left( e ^ { x } \right)$