  In string theory compactifications it is common to find an effective
Lagrangian for the scalar fields with a non-canonical kinetic term. We study
the effective action of the scalar position moduli of Type II D$p$-branes. In
many instances the kinetic terms are in fact modified by a term proportional to
the scalar potential itself. This can be linked to the appearance of
higher-dimensional supersymmetric operators correcting the K\"ahler potential.
We identify the supersymmetric dimension-eight operators describing the
$\alpha'$ corrections captured by the D-brane Dirac-Born-Infeld action. Our
analysis then allows an embedding of the D-brane moduli effective action into
an $\mathcal N = 1$ supergravity formulation. The effects of the
potential-dependent kinetic terms may be very important if one of the scalars
is the inflaton, since they lead to a flattening of the scalar potential. We
analyze this flattening effect in detail and compute its impact on the CMB
observables for single-field inflation with monomial potentials.
