I'm not sure how to take the derivative of $\displaystyle e^{x^2}$

according to this:

it is $\displaystyle e^{x^2}*2x$ (using l'hospital's rule) but how did they get that? when I plug it into maple I get $\displaystyle 2e^{x^2}x ln(e) $ which is the same as what is above (given that ln(e) =1) but I don't knowwhythat should be the answer.