Find the Derivative Of $f ( x ) = \left\{ \begin{array} { c l } \ln ( x + 3 ) & \text { if } x < 1 \\4 x ^ { 2 } - 1 & \text { if } x \geq 1\end{array} \right.$

Multiple Choice

Find the derivative of $f ( x ) = \left\{ \begin{array} { c l } \ln ( x + 3 ) & \text { if } x < 1 \\4 x ^ { 2 } - 1 & \text { if } x \geq 1\end{array} \right.$

A) $f ^ { \prime } ( x ) = \left\{ \begin{array} { c l } \frac { 1 } { x + 3 } & \text { if } x < 1 \\4 x ^ { 2 } + 1 & \text { if } x \geq 1\end{array} \right.$
B) $f ^ { \prime } ( x ) = \left\{ \begin{array} { c l } \frac { 1 } { x + 3 } & \text { if } x < 1 \\\text { DNE } & \text { if } x = 1 \\4 x & \text { if } x > 1\end{array} \right.$
C) $f ^ { \prime } ( x ) = \left\{ \begin{array} { c c } \frac { 1 } { x + 3 } & \text { if } x < 1 \\8 x & \text { if } x \geq 1\end{array} \right.$
D) $f ^ { \prime } ( x ) = \left\{ \begin{array} { c l } \frac { 1 } { x + 3 } & \text { if } x < 1 \\\text { DNE } & \text { if } x = 1 \\8 x & \text { if } x > 1\end{array} \right.$