Let $f$ be the function defined by $f ( x ) = e ^ { 2 x }$. Which of the following is the Maclaurin series for $f ^ { \prime }$, the derivative of $f$?\\
(A) $1 + x + \frac { x ^ { 2 } } { 2 ! } + \frac { x ^ { 3 } } { 3 ! } + \cdots + \frac { x ^ { n } } { n ! } + \cdots$\\
(B) $2 + 2 x + \frac { 2 x ^ { 2 } } { 2 ! } + \frac { 2 x ^ { 3 } } { 3 ! } + \cdots + \frac { 2 x ^ { n } } { n ! } + \cdots$\\
(C) $1 + 2 x + \frac { ( 2 x ) ^ { 2 } } { 2 ! } + \frac { ( 2 x ) ^ { 3 } } { 3 ! } + \cdots + \frac { ( 2 x ) ^ { n } } { n ! } + \cdots$\\
(D) $2 + 2 ( 2 x ) + \frac { 2 ( 2 x ) ^ { 2 } } { 2 ! } + \frac { 2 ( 2 x ) ^ { 3 } } { 3 ! } + \cdots + \frac { 2 ( 2 x ) ^ { n } } { n ! } + \cdots$