We study the derivative expansion for the effective action in the framework
of the Exact Renormalization Group for a single component scalar theory. By
truncating the expansion to the first two terms, the potential Uk and the
kinetic coefficient Zk, our analysis suggests that a set of coupled
differential equations for these two functions can be established under certain
smoothness conditions for the background field and that sharp and smooth
cut-off give the same result. In addition we find that, differently from the
case of the potential, a further expansion is needed to obtain the differential
equation for Zk, according to the relative weight between the kinetic and
the potential terms. As a result, two different approximations to the Zk
equation are obtained. Finally a numerical analysis of the coupled equations
for Uk and Zk is performed at the non-gaussian fixed point in D<4
dimensions to determine the anomalous dimension of the field.Comment: 15 pages, 3 figure