1. By carefully showing all your steps, differentiate the function f(x) = (tan 1(x + v=))4 2. Fine powdered icing sugar pours down from a dispensing chute at a constant rate of 3 mo/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. A particle moves on the line y = 2x + 1 in such a way that its r-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 r-axis, the line connecting the particle to the origin, and the r-axis. At what rate is the area of the right triangle changing when r = 4? 4. Suppose that ri + yi = 2. What is y" at the point (1, 1)? 5. If f(:) = In(x + In(=)) determine f'(1). Be careful to show all your work