1. Consider the function defined by f(x) = In(Vx)). . (1 mark) State the domain of this function. . (2 marks) Determine the derivative of In(V(x|). Be careful to show all your work. 2 . (3 marks) If f(x) = In(x + In(x)) determine f' (1). Be careful to show all your work. 3. (3 marks) Gravel is being dumped from a conveyor belt at a rate of 25fts / min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is (a) 10 ft high? (b) 15 ft high