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Derivative of cosh inverse x

  1. Nov 10, 2007 #1
    1. The problem statement, all variables and given/known data

    Derive cosh[tex]^{-1}[/tex]x

    2. Relevant equations

    None I know of.
    3. The attempt at a solution

    Well I vaguely remember that the inverse of this was something like

    ln(x + [tex]\sqrt{x^2 - 1}[/tex])

    If I derive this, I will get [tex]\frac{1}{\sqrt{x^2 - 1}}[/tex]

    Is that correct? Am I wrong to assume the equation for the inverse of cosh? Or do I need to prove that as well
     
  2. jcsd
  3. Nov 11, 2007 #2

    rock.freak667

    User Avatar
    Homework Helper

    actually...[tex]\frac{d}{dx}arccoshx=\frac{1}{\sqrt{x^2-1}}[/tex]

    prove it by just letting y=arccoshx and then putting coshy=x and findind dy/dx
    and use the identity cosh^2(x)-sinh^2(x)=1
     
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