Let f(u, v) be a smooth function such that fu(4,4)= f,(4,4) = 1 and let g(x, y, z) = f(xy, yz). Let w be the unit vector in the direction in which g(x, y, z) increases the fastest at (x, y, z) = (1,4, 1). Find the rate of change of g at the point (1,4, 1) in the direction of W.