# Thread: taking the derivative of e^(x^2)

1. ## taking the derivative of e^(x^2)

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 know why that should be the answer.

2. ## Re: taking the derivative of e^(x^2)

Originally Posted by kingsolomonsgrave
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 know why that should be the answer.
Have a look here: Chain rule - Wikipedia, the free encyclopedia

3. ## Re: taking the derivative of e^(x^2)

OH, I did not realize that the chain rule would apply to an exponent that is itself a function of x. thanks

also I meant they were applying l'hospital's rule to the entire expression, not to $\displaystyle e^{x^2}$

100th post!