a) Assume z = f (u, 12) is a differentiable function and g(x, y) = f (x2 + yz, xy). Find 3: . . . . . . a a and . (Hlnt: Your answer Will involve the partial derivatives i and ai. b) Now assume 3324) = 4, 6{(2,1) = 2, aj:(5,2) = 2 and 3:(52) = 1. Use your answer to part a) to nd 3: (2,1) and 3: (2,1). The position ofan object at time t Z 0 is given by (x(t),y(t)) = (3cos(t), 45in (15)), 0 g t S 27L a) Sketch the path of the object's motion. b) Let D (x, y) denote the distance from a point (x, y) to the origin. What does D (x (t), y(t)) represent as 0 S t S 21!? c) Now use the multivariable chain rule to determine how fast the object is moving away from (or approaching) the origin when t = E. d) How fast is the object moving away from (or approaching) the origin when t = Bit/4