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Homework Help: Differentiation of Ln(x+1/x)

  1. Nov 2, 2008 #1
    Hi all,

    I have to differentiate


    where I first differentiate Ln and than multiply by the differentiation of the inner function


    which I simplify to



    the problem is I cannot rewrite it to this


    how to rewrite it - any help or advise appreciated. Thanks in advance

    Last edited: Nov 2, 2008
  2. jcsd
  3. Nov 2, 2008 #2
    Start at the final expression, and write it as a fraction with one denominator: x(x^2+1)
  4. Nov 2, 2008 #3

    so I put into one fraction


    but I don't know how to start rearranging this.... Any new hints


  5. Nov 2, 2008 #4


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    [itex]x^2-1=(x^2+1)-2[/itex] ;0)
  6. Nov 2, 2008 #5
    so I rewrite the fraction using this hint


    I split the fraction into


    but I can still not see how to rearrange it

    Thanks in advance

  7. Nov 2, 2008 #6


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    Use partial fractions to decompose your second term; in other words, find the constants [itex]A[/itex],[itex]B[/itex], and [itex]C[/itex] that satisfy:

  8. Nov 3, 2008 #7
    In what form do you want it? Whether it is condensed into one fraction or written as a difference doesn't matter if both expressions are equal.
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