1. Suppose f (x, y) = (x y)exy. Let u = (1, 1). Find the directional derivative of f at the point (3, 0) in the direction of the vector u. Then give a unit vector v for which Dvf (3, 0) = 0.

2. Suppose that z is implicitly defined by the equation y2z + z3 + 2sin(z) = x sin(2x + y). Use implicit differentiation to give a formula for z x in terms of x, y, and z.