1. (3 marks) By carefully showing all your steps, differentiate the function f (2) = (tan -'(x + Vx))4 2. (3 marks) Fine powdered icing sugar pours down from a dispensing chute at a constant rate of 3 m3 / min. The sugar pile forms on the floor in the shape of a cone with a height that is twice the base radius. What is the rate of change of the height of the sugar pile at the instant the height is a) 2 m? b) 5 m? 3. (3 marks) A particle moves on the line y = 2x + 1 in such a way that its x-coordinate changes at a constant rate of 4 units per second. A right triangle is formed by the vertical line from the particle to the x-axis, the line connecting the particle to the origin, and the x-axis. At what rate is the area of the right triangle changing when x = 4? 4. (3 marks) Suppose that x7 + ya = 2. What is y" at the point (1, 1)? 5. (3 marks) If f(x) = In(x + In(x)) determine f' (1). Be careful to show all your work