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Derivative of inverse hyperbolic functions

  1. Jan 29, 2009 #1
    1. The problem statement, all variables and given/known data
    I don't understand how to take the derivative of inverse hyperbolic functions such as sinh[tex]^{-1}[/tex](x). I know that the derivative of sinh(x) is cosh(x) but don't know what to do with the inverse.

    2. Relevant equations

    3. The attempt at a solution
    I'm completely at a loss here. Could somebody point me in the right direction? (I don't necessarily want the answer, just a shove along the path would be wonderful)
  2. jcsd
  3. Jan 29, 2009 #2


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    Welcome to PF!

    Hi mvantuyl! Welcome to PF! :smile:

    Hint: if y = sinh-1x, then write x = sinhy, and then differentiate (and then convert back into x's, of course)! :wink:
  4. Jan 29, 2009 #3
    Re: Welcome to PF!

    Thank you! It's so obvious I managed to completely overlook it. :)
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