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Differentiation Question Concerning natural log

  1. Jan 19, 2005 #1
    Hello all

    If [tex] y = e^3^\ln^(x^2) [/tex] find [tex] \frac {dy}{dx} [/tex]

    So [tex] \frac {dy}{dx} =(3 (\frac {1}{x^2}) \* 2x e^3^\ln^(x^2) [/tex]

    So the simplified answer is: [tex] \frac {6}{x} e^3^\ln^(x^2) [/tex]

    Is this correct? IS there any other way of expressing the answer?

    Thanks
     
  2. jcsd
  3. Jan 19, 2005 #2

    chroot

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    Use your log rules.

    [tex]e^{3 \ln x^2} \equiv e^{\ln x^6} \equiv x^6[/tex]

    - Warren
     
  4. Jan 19, 2005 #3
    oh i see

    So derivative would be [tex] 6x^5 [/tex]

    didn't catch that

    thanks
     
  5. Jan 19, 2005 #4

    chroot

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    Pretty much anytime you see e and ln stuck together like that, it means your teacher is trying to get you to use log rules.

    - Warren
     
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