Let $f : \mathbb { R } \rightarrow [ 0 , \infty )$ be a continuous function such that
$$f ( x + y ) = f ( x ) f ( y )$$
for all $x , y \in \mathbb { R }$. Suppose that $f$ is differentiable at $x = 1$ and
$$\left. \frac { d f ( x ) } { d x } \right| _ { x = 1 } = 2$$
Then, the value of $f ( 1 ) \log _ { e } f ( 1 )$ is\\
(A) $e$.\\
(B) 2.\\
(C) $\log _ { e } 2$.\\
(D) 1 .