Problem 3. (a) Suppose z = f(r, y) has continuous partial derivatives. Let x = rcos(@) and y = rsin(0). We want to compute the partial deriva- tives of f(x(r, 0), y(r, 0)) with respect to r and 0. Explain why we have of of ar = cos(0) + sin(0) of dy and, further, of of ae = -r sin(0) fe ar + r cos(0) ay Finally, show that 2 2 2 of of + + ay 2 (b) Let f(x, y) = In(x2 + y?). Use (a) to compute af dy 2 2 (c) Let g(x, y) = evasty' . Use (a) to compute @g + ag dy