1617-257/TUT-R-6

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.

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