Suppose That $g ( x )$ Is a Differentiable Function $f ^ { \prime } ( x )$

Essay

Suppose that $g ( x )$ is a differentiable function. Find $f ^ { \prime } ( x )$ for each of the following, in terms of $g ( x )$ and $g ^ { \prime } ( x )$ .(a) $f ( x ) = e ^ { x } g ( x )$ (b) $f ( x ) = \frac { 3 x - 1 } { g ( x ) }$ (c) $f ( x ) = g ( x ) \left( 3 x ^ { 2 } - 8 \right)$ (d) $f ( x ) = \sqrt { x } ( g ( x ) + 4 )$