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Math Help - taking the derivative of e^(x^2)

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

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

    according to this: taking the derivative of e^(x^2)-screen-shot-2012-11-14-1.32.24-am.png

    it is e^{x^2}*2x (using l'hospital's rule) but how did they get that? when I plug it into maple I get  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.
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    Re: taking the derivative of e^(x^2)

    Quote Originally Posted by kingsolomonsgrave View Post
    I'm not sure how to take the derivative of e^{x^2}

    according to this: Click image for larger version. 

Name:	Screen Shot 2012-11-14 at 1.32.24 AM.png 
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    it is e^{x^2}*2x (using l'hospital's rule <-- ??) but how did they get that? when I plug it into maple I get  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
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    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 e^{x^2}


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