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Derivative of a fraction?

  1. Mar 31, 2008 #1
    How do I take the derivative of

    f(x)=ln[x/(x-1)]?

    Thanks!
     
  2. jcsd
  3. Mar 31, 2008 #2

    tiny-tim

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    Welcome to PF!

    Hi lreichardt! Welcome to PF! :smile:

    Just use the chain rule: derivative of ln, times the derivative of x/(x-1). :smile:
     
  4. Mar 31, 2008 #3
    so, (x/1)(quotient rule of x/(x-1)? =

    (x/1)(-x/x-1)=-x^2/x-1
     
  5. Mar 31, 2008 #4

    tiny-tim

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    ooh dear …

    better go the easy way … simplify it first …

    ln(x/(x-1)) = ln(x) - ln(x-1) … now differentiate! :smile:
     
  6. Apr 6, 2008 #5
    Chain rule = The difference of the derivative of the "Outer" and derivative of the "Inner", put simply.
     
  7. Apr 6, 2008 #6
    Thanks all, figured it out.
     
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