Exercise 1 Determine whether of the following are exact differentials. (a) 6xy3dx + 9x2y-dy (b) (1/y) dx - (x/y2) dy Let z = e'cos(0) with r = st and 0 = vs2 + 2, calculate the following derivatives: (c) oz as (d) oz at (e) azz as2 Calculate the following vector expressions: (f) Vf for f = tan (3x - 4y) (g) div(7) for (x, y, z) = xyi + yz2j + x2yzk (h) curl(u) for u(x, y, z) = xzi + xy?j + y2zk