It is well known that the product rule for the exterior derivative reads [tex]d(a\wedge b)=(da)\wedge b +(-1)^p a\wedge (db),[/tex]where a is a p-form. In gauge theory we then introduce the exterior covariant derivative [tex]D=d+A\wedge.[/tex] What is then D(a ∧ b) and how do you prove it? I obtain [tex]D(a\wedge b)=d(a\wedge b)+A\wedge a \wedge b=(da)\wedge b +(-1)^p a\wedge (db)+A\wedge a \wedge b,[/tex] which is neither (Da) ∧ b +(-1)p a ∧ (Db) nor (Da)∧ b + a∧ (Db). I have, however, seen the latter been used without proof.