The origin of the functional properties of complex oxide superlattices can be resolved using time-resolved synchrotron x-ray diffraction into contributions from the component layers making up the repeating unit. The CaTiO3 layers of a CaTiO3/BaTiO3 superlattice have a piezoelectric response to an applied electric field, consistent with a large continuous polarization throughout the superlattice. The overall piezoelectric coefficient at large strains, 54 pm/V, agrees with first-principles predictions in which a tetragonal symmetry is imposed on the superlattice by the SrTiO3 substrate.