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Derivative of an exponential function using logarithms (lon-capa)

  1. Feb 29, 2012 #1
    1. The problem statement, all variables and given/known data

    What is the derivative of y=x^(13/x^2) with respect to x?


    3. The attempt at a solution

    I went through multiple techniques to solve this, but all of them have failed so far ._.

    In my latest attempt, I took the natural log of both sides:

    lny= lnx^(13/x^2)

    I then brought the exponent out of the natural log:

    lny = 13/x^2*lnx = 13/x^2 * 1/x = 13/x^3

    And solved for both natural logs:

    1/y*dy/dx = 13/x^3

    dy/dx = x^(13/x^2)*(13/x^3)

    Lon-capa says this is wrong. It also says that the other method I used is wrong:

    d/dx = a^x*ln(a)

    x^(13/x^2)*ln(x)*(-26/x^3)

    Please help me~
     
  2. jcsd
  3. Feb 29, 2012 #2
    This problem is due in 25 mins so I'm shamelessly bumping it up ._.
     
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