  We present some explicit computations checking a particular form of gradient
formula for a boundary beta function in two-dimensional quantum field theory on
a disc. The form of the potential function and metric that we consider were
introduced in hep-th/9210065, hep-th/9311177 in the context of background
independent open string field theory. We check the gradient formula to the
third order in perturbation theory around a fixed point. Special consideration
is given to situations when resonant terms are present exhibiting logarithmic
divergences and universal nonlinearities in beta functions. The gradient
formula is found to work to the given order.
