Differentiate the Following Functions:
(A) $f ( x ) = x ^ { 3 } e ^ { x }$

Essay

Differentiate the following functions:
(a) $f ( x ) = x ^ { 3 } e ^ { x }$ (b) $g ( x ) = \frac { x ^ { 2 } + 1 } { x ^ { 2 } - 1 }$ (c) $h ( x ) = \frac { e ^ { x } } { e ^ { x } + 1 }$ (d) $\varnothing ( x ) = \left( 1 - \frac { 1 } { x } \right) ^ { 2 }$