50. Polar coordinates Suppose that we substitute polar coordi- nates x = r cos 0 and y = r sin 0 in a differentiable function w = f(x, y). a. Show that дw f, cos 0 + f, sin 0 дr and 1 dw -fx sin 0 + f, cos 0. b. Solve the equations in part (a) to express fr and f, in terms of ôw/ðr and ðw/d0. c. Show that (G,F + (5, = () + +(). дw 12 a0

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