Derivative of inverse hyperbolic functions

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To find the derivative of the inverse hyperbolic function sinh^{-1}(x), start by letting y = sinh^{-1}(x), which implies x = sinh(y). Differentiate both sides with respect to x, leading to the relationship between the derivatives. After differentiating, convert back to express the derivative in terms of x. This approach simplifies the process of finding the derivative without directly applying the inverse function rules.
mvantuyl
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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)
 
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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:
 


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

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