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Office_Shredder

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^{-1}(x), followed up by the derivative of ln( x + sqrt(1+x

^{2}) ). In high school, we never really covered hyperbolic trigonometry, but I have previously derived that the inverse of sinh is ln( x + sqrt(1+x

^{2}) ), and used that fact to solve for the derivative of sinh

^{-1'}(by taking the derivative of the ln term)

The trouble i'm having is that it seems obvious that you weren't supposed use the ln term to solve for the derivative, otherwise they wouldn't have posed both questions next to each other. So my guess is that there's some alternative method through which you can solve for this that I may need to know for the school year. If anyone has any ideas, that would be great.