Let $f:\mathbb{R}\to [0,\mathrm{\infty })$ 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 $${\frac{df(x)}{dx}|}_{x=1}=2$$ Then, the value of $f(1){\log }_{e}f(1)$ is