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Derivatives of ln functions

  1. Apr 5, 2008 #1
    product rule


    but answer in book is f'(x)=3x^2(lnx^2)+2x^2
    What am i doing wrong?
  2. jcsd
  3. Apr 5, 2008 #2
    What's the derviative of just ln(x)?
  4. Apr 6, 2008 #3
    x has an exponent of 1
  5. Apr 6, 2008 #4
    d/dx lnx = 1/x
  6. Apr 6, 2008 #5
    So does the derivative of lnx^b not = blnx?
  7. Apr 6, 2008 #6
    ln(x^b) = b * ln(x)

    This is a property of logarithms and has nothing to do with differentiation.

    d/dx [b * ln(x)] = b/x
  8. Apr 6, 2008 #7
    You can also find the derivative if you use a u-sub rather than simplifying the natural log. You might notice that the 1 in the numerator is the derivative of the denominator.

    Try [tex] \frac{u'}{u}[/tex]
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