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Math Help - Derivative Problem

  1. #1
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    Derivative Problem

    Im pretty sure i did the derivative part right but i just want a second take on my algerbra

    \frac {e^{x^2}}{1+ \ln x}


     \frac {dy}{dx} = 1 + \ln x * e^{x^2} *2x - e^{x^2} * \frac {1}{x}

    = 2x(1 + \ln x ) * e^{x^2} - \frac {e^{x^2}}{x}
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  2. #2
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    Quote Originally Posted by x5pyd3rx View Post
    Im pretty sure i did the derivative part right but i just want a second take on my algerbra

    \frac {e^{x^2}}{1+ \ln x}


     \frac {dy}{dx} = 1 + \ln x * e^{x^2} *2x - e^{x^2} * \frac {1}{x}

    = 2x(1 + \ln x ) * e^{x^2} - \frac {e^{x^2}}{x}


    It's wrong: the quotient derivative's rule is \left(\frac{u}{v}\right)'=\frac{u'v-uv'}{v^2}.

    Apparently you forgot the denominator...

    Tonio
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  3. #3
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    Jeez i feel dumb but the algerbra on top is correct and all i would do is throw the (1 + ln x)^2 on the bottom.

    you would think someone taking calc 2 would know the quotient rule
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  4. #4
    Super Member Random Variable's Avatar
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    It's technically never necessary to use the quotient rule because it's just a form of the product rule.
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  5. #5
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    Ya i thought of that to after i did the problem.
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  6. #6
    Super Member Random Variable's Avatar
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     \frac{d}{dx} \ \frac{e^{x^{2}}}{1+ \ln(x)} = \frac{2xe^{x^{2}}}{1+\ln(x)} + e^{x^{2}} *\frac{-1}{(1+\ln(x))^{2}}*\frac{1}{x}
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  7. #7
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    Woah .... so wait.. our answers are the same correct you just simplified yours more correct?
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  8. #8
    Super Member Random Variable's Avatar
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    Quote Originally Posted by x5pyd3rx View Post
    Woah .... so wait.. our answers are the same correct you just simplified yours more correct?
    Yes, our answers are the same. I can simplify mine so that it looks like yours. I just wanted to show how you can use the product rule instead of the quotient rule.
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  9. #9
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    Quote Originally Posted by Random Variable View Post
    Yes, our answers are the same. I can simplify mine so that it looks like yours. I just wanted to show how you can use the product rule instead of the quotient rule.
    back in school i always used the product rule to get around the quotient rule. but as of now, i am indifferent to them and consider the quotient rule to be so damn simple to remember.
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