Prove the following. Let M C R be a smooth surface, let Z, Y: M R be smooth vector fields, let f: M R be a smooth function, let p E M be a point, let u, w E TM be vectors and let a, b be real numbers. Then (i) av+bwZ = aZ + bZ. (ii) (Z+Y) = VZ + VY (iii) vZ = ()Z(p) + (p)(vZ). (iv) (Z,Y) = (Z,Y(p)) + (Z(p), Y).