6. (a) Suppose z = f(x, y) has continuous partial derivatives. Let r = rcos0 and y = rsin0. We want to compute the partial derivatives of f(x(r, 0), y(r, 0)) with respect to r and 0. Explain why we have of = cos 0- of + sin 0 of ar ay and of -r sin 0 of + r cos 0 of ay Show that of ar + ae a + ( 35 ) (b) Let f(x, y) = In(x2 + y') which simplifies when you plug in r = rcose and y = rsind. Use af 2 2 part (a) to compute + a ay 1