Limit using L'hospital and maybe another trick

Hi, I've been sitting on this more than an hour and still can't find the solution :(

I put this in a function grapher and it looks like the result should be , but I don't understand why this is true or how do I get to this solution. I assume that L'hospital should be used and supposedly there's another trick?

Thanks in advance

Simplifying the derivation

Actually, you can greatly simplify the derivation if you put y=1/x in the limit.

so as

the equation becomes

applying l'hospital's rule, we get

which is

Since the left hand side is e, we apply l'hospital again to the right side

Applying l'hospital again, we get