1. The problem statement, all variables and given/known data We have a vector X^a (n.b ^ indicates superscript) and covector Aa. We need to show that X^b (d(Aa)/d(x^b) - d(Ab)/d(x^a)) transforms correctly under an artbitrary smooth change of coords. N.b the derivatives are partial. By using the transformation rules for the vector and covector respectively I get four terms, two of which give us the required transformation rule. I can't get the other two to disappear. I'd appreciate any hints.