Higher derivative terms are computed in the one-loop effective action governing the interactions of D3-branes, in two ways: (1) in a formalism with N=2 supersymmetry preserved off-shell, and (2) in the standard background field formalism, with only on-shell supersymmetry. It is shown that these calculations only agree using tree-level equations of motion. The off-shell supersymmetric calculation exhibits acceleration terms that appear in terms with four derivatives. These may imply disagreement at two-loop order between supergravity and Yang-Mills descriptions of D-brane dynamics.

11 pages, LaTeX. Minor wording changes