  The perturbative evaluation of the effective action can be expanded in powers
of derivatives of the external field. We apply the renormalization group
equation to the term in the effective action that is second order in the
derivatives of the external field and all orders in a constant external field,
considering both massless scalar $\phi_4^4$ model and massless scalar
electrodynamics. A so-called ``on shell'' renormalization scheme permits one to
express this ``kinetic term'' for the scalar field entirely in terms of the
renormalization group functions appropriate for this scheme. These
renormalization group functions can be related to those associated with minimal
subtraction.
