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taking the derivative of e^(x^2)

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

according to this: Attachment 25704

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.

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

Quote:

Originally Posted by

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

according to this:

Attachment 25704
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

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!(Clapping)