  We consider the Burgers equation on $H=L^2(0,1)$ perturbed by white noise and
the corresponding transition semigroup $P_t$. We prove a new formula for
$P_tD\varphi$ (where $\varphi:H\to\R$ is bounded and Borel) which depends on
$\varphi$ but not on its derivative. Then we deduce some new consequences for
the invariant measure $\nu$ of $P_t$ as its Fomin differentiability and an
integration by parts formula which generalises the classical one for gaussian
measures.
