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Homework Help: Derivative x^(lnx)

  1. Dec 10, 2006 #1
    1. The problem statement, all variables and given/known data
    y=x^(lnx) i know the derivative of lnx is 1/x but what about x^(lnx)?

    ln(cos-¹x)


    2. Relevant equations
    N/A


    3. The attempt at a solution

    ln(cos-¹x) (1/(cos-¹x))(-x/√(1-x²)) -x/(cos-¹x√(1-x²))
    The back in the book has the same answer except the -x is a -1 instead.
     
  2. jcsd
  3. Dec 11, 2006 #2
    Where did the cos-1x come from? :confused:

    Usually, when you want to differentiate a function of the form f(x)^g(x), it helps to take the logarithm of the function and then find the derivative.

    y = x^ln(x)

    ln(y) = ln(x^ln(x))...
    Can you do it from here?
     
  4. Dec 11, 2006 #3
    on the ln(cos^-1x) is a different question.
     
  5. Dec 11, 2006 #4
    Oh, okay. There is a -1 because the derivative of arccos(x) is -1/sqrt(1-x^2).
     
  6. Dec 11, 2006 #5
    k I got the first one but i dont get the second one.(ln(cos-¹x))
     
  7. Dec 11, 2006 #6
    k nm I got it thx
     
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