Exercise 3: Here we will compute using the directional derivative Dvf = V v/||v||. (a) Compute the directional derivative with f(x, y) = x cos(xy) and v = [21]T. = (b) You are goat climbing a mountain, where the altitude is given by the function f(x, y) 5 x y. To impress the humans below, you want to choose the steepest path up the mountain. You are at the point (1,1,3). What direction should you go in to climb the steepest path? = (c) You are a cold mosquito flying around a room. The temperature is given by T(x, y, z) cos(x) sin(y) cos(2), and you are at the point (1,2, 1). What direction should you fly to warm up?