1. Suppose that u = u(x,y), x(r.0) rcos 8, y(r, 0) = r sin 0, and Myy = yx- (a) (2 points) Use the Multivariable Chain Rule to prove that. 1, (b) (4 points) Use part (a) to prove that cosu,+ sin uy y = cos xx + 2 sin cos xy + sin uyy (Hint: Assume that rrx and yr Ury.) (e) (2 points) Use the Multivariable Chain Rule to prove that Mersin 0, +r cos e uy (d) (4 points) Use part (c) to prove that: ugg = r² sin²0x+r² cos² 0 Myy - 2r2 sin cos xy-rcos ux-r sine uy (Hint: Assume that yg uex and ye May.) (e) (3 points) Use parts (a), (b), and (d) to prove that: 1 1 ++= 4xx + Myy