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On 10/20/16, we discussed how one can calculate the derivative of the inverse of the map f: (0,1/2) \times (0, \pi/4) \to U \subset \mathbb R^2 where f(r, \theta) := (r \cos \theta, r \sin \theta):

Method 1. Find f^{-1} explicitly and differentiate it.

Method 2. Use the inverse function theorem.

Students who did both calculations noted that Method 2 was simpler than Method 1.