The derivative expansion of the one-loop effective Lagrangian in QED_3 and QED_4 is considered. The first term in such an expansion is the Schwinger's result for a constant electromagnetic field. An explicit expression for the next term containing two derivatives of the field strength with respect to space-time coordinates is obtained. The general results for both fermion and scalar electrodynamics are presented. The cases of pure electric and pure magnetic external fields are considered in details. The Feynman rules for the perturbative expansion of the one-loop effective action in the number of derivatives are presented.