$\displaystyle \lim{x}\rightarrow{\infty} \frac{(1+x)^{\frac{1}{x}}-e}{x}$

well the answer is -e/2, but I can't seem to get the answer...mostly due the fact that there is a 1/x power on the 1+x polynomial and how to implement it with

L'Hopitale's rule...?