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Need some help differentiating

  1. Mar 28, 2008 #1
    [SOLVED] need some help differentiating

    Uh my bad, forgot how to differentiate ln's

    1. The problem statement, all variables and given/known data
    [tex]\frac{V_0}{xln(\frac{b}{x})} [/tex]
    Find dE/dx

    I can almost get the answer, but I had to use matlab to find the actual answer, so I am kind of feeling stupid now.

    My problem is when I try to differentiate the ln

    2. Relevant equations

    3. The attempt at a solution

    [tex]d/dx(\frac{V_0}{xln(\frac{b}{x})}) = \frac{-V_0}{x^2 ln(b/x)} + \frac{V_0 * b/x^2}{x ln(b/x)^2} =[/tex]

    [tex]\frac{-V_0}{x^2 ln(b/x)} + \frac{V_0 * b}{x^3 ln(b/x)^2}[/tex]

    The second term should only have x^2 in it (and no b), does anyone see where I went wrong?
    Last edited: Mar 28, 2008
  2. jcsd
  3. Mar 28, 2008 #2
    [tex]log_a(x)=y=>a^{y}=x[/tex] let's differentiate this implicitly, we get:


    When a=e, we get:[tex]\frac{dy}{dx}=\frac{1}{x}[/tex]. So it is just a special case of a general case.
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