# Derivative of inverse hyperbolic functions

1. Jan 29, 2009

### mvantuyl

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$$^{-1}$$(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. Jan 29, 2009

### tiny-tim

Welcome to PF!

Hi mvantuyl! Welcome to PF!

Hint: if y = sinh-1x, then write x = sinhy, and then differentiate (and then convert back into x's, of course)!

3. Jan 29, 2009

### mvantuyl

Re: Welcome to PF!

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