1. If z = f(x, y) and fx(2, 3) = 2, fy(2, 3) = 9 , find dz/dt at t = 2 when x = g(t), y = h(t) and g(2) = 2 , g (2) = 3 . h(2) = 3 , h (2) = 4 .

2. The length and width w of the closed box shown in h w are increasing at a rate of 2 ft/min while its height h is decreasing at a rate of 3 ft/min. Find the rate at which the volume of the box is increasing when = 5 , w = h = 3 feet

3.If z = f(x, y) and x = r cos 2 , y = 2r sin , express z in terms of z /x and z/ y .

4.The radius of a right circular cylinder is decreasing at a rate of 4 inches per minute while the height is increasing at a rate of 6 inches per minute. Determine the rate of change of the volume when r = 5 and h = 5.

5. Use the Chain Rule to find z /s when z = x 2 + 2xy + y 2 , and x = 3s 2t , y = st .