Derivative of inverse hyperbolic functions

[mvantuyl]

Homework Statement

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.

Homework Equations

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)

 

[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)!

 

[mvantuyl]

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