1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Homework Helper
    Gold Member

    [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


    User Avatar
    Homework Helper
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook