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Deriving the formula for arctanh(x)

  1. Aug 19, 2008 #1
    1. The problem statement, all variables and given/known data

    "starting from the definition of tanhx in terms of exponentials, prove that...

    arctanh(x)=1/2log((1+x)/(1-x))

    This is such a simple equation but I'm having a hard time proving it, can anyone help?

    Cheers


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 19, 2008 #2

    HallsofIvy

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    If y= tanh(x) then
    [tex]y= \frac{e^x- e^{-x}}{e^x+ e^{-x}}[/tex]
    Now use the standard method of finding an inverse function: solve that equation for x.
     
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