I have a following problem. Let D be an operator taking the C^oo functions F to F, and the C^oo vector fields V to V, such that D:F-->F and D:V-->V, are linear over R(real) and D(f Y) = f * DY+Df * Y. Here * is a multiplication Show that D has a unique extension to an operator taking tensor fields of type(k, l) to themselves such that (1) D is linear over R(real). (2) D(A $ B)= DA $ B+ A $ DB. Here $ is a tensor product. (3) for any contraction C, DC=CD. If you have Spivak's geometry book. This is a problem 5-15. Any help would be appreciated. Thanks.