  We introduce the notion of the Drinfeld dual of an algebra and show that Hall
algebras defined by Kontsevich-Soibelman in \cite{KS} are the Drinfeld duals of
derived Hall algebras defined in \cite{Toen2005} and \cite{XX2006}. Moreover,
we construct the motivic analogue of a derived Hall algebra and prove that it
is isomorphic to the motivic Hall algebra constructed in \cite{KS}.
