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Derivatives question

  1. Mar 24, 2009 #1

    I'm trying to find the derivative of [tex]-ln(-\Theta)[/tex] with respect to [tex]\Theta[/tex]

    The answer's [tex]-\frac{1}{\Theta}[/tex]

    I'm not sure why though. Here's my working.

    [tex]\frac{d}{d\Theta} -ln(-\Theta)[/tex]

    [tex] = \frac{d}{d\Theta} ln(-\frac{1}{\Theta})[/tex]

    [tex] = -\Theta[/tex]

    Can anyone explain where I'm going wrong? Thanks.
  2. jcsd
  3. Mar 24, 2009 #2
    = - d(ln(-th))/dth
    = - (-th)^(-1) d(-th)/dth
    = - (-th)^(-1) (-1)
    = - (1/th)
  4. Mar 24, 2009 #3
    You need to apply the chain rule. The derivative of [tex]-\frac{1}{\Theta}[/tex] is [tex]\frac{1}{\Theta^2}[/tex]. If you multiply this with [tex]-\Theta[/tex] you get the correct answer.
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