Is there a simple formula for the action of the codifferential on a wedge product of forms
$d^\dagger (a \wedge b) = *d*(a \wedge b)$?
I was hoping for something like
$d^\dagger (a \wedge b) = (d^\dagger a) \wedge b + (-1)^p a \wedge (d^\dagger b)$
but that doesn't seem to be true.