2. (a) Find the directional derivative of f in the direction v at the point (1, 0, 0) where f(x, y, z) = x ² e ^y+z and v = (1, 1, 1).

(b) Evaluate (closed integral) F dr where F = (xy, x² + y ² ) and C is the arc of y = x ² connecting (1, 1) and (2, 4).

(c) Verify the chain rule (second special case) for f(x, y, z) = (x ² y, xy, xz) and g(s, t, u) = (st, tu, su).