limits - Application of l'hospital rule to exponential function

The assignment I got is to solve the limit below using l'hospital's rule.

$$\lim_{x\to\infty} e^{x-x^2}$$

What I did was turn it into a quotient

$$\lim_{x\to\infty} \frac{e^{x}}{e^{x^2}}$$

So now we have the indeterminate form $\frac{\infty}{\infty}$ and apply l'hospital's rule

$$\lim_{x\to\infty} \frac{e^{x}}{2 e^{x^2}x}$$

I re-applied it a few times, but it appears that it cannot be solved this way.

My question is how can this be solved with l'hospital's rule? Please provide explanation or hint on how it can be worked out, I don't need a plain answer.