[hervature]

I think these questions are meant to really address mechanical skills. The second question took me 7 differentiations. It takes understanding to be able to do that but the rate of error is going to be very high even for those that understand differentiation perfectly.

Edit: someone posted a link showing that one can generalize this result for g, f and their inverses. Interestingly, after reading up on it, the point Arnold is trying to make is that modern students have a poor grasp of infinitesimals.