  We use compatibility of D-brane action with linear T-duality, S-duality and
with S-matrix elements as guiding principles to find all world volume couplings
of one massless closed and two open strings at order $\alpha'^2$ in type II
superstring theories. In particular, we find that the squares of second
fundamental form appear only in world volume curvatures, and confirm the
observation that dilaton appears in string frame action via the transformation
$\hat{R}_{\mu\nu}\rightarrow \hat{R}_{\mu\nu}+\nabla_{\mu}\nabla_{\nu}\Phi$.
