A novel quantitative phase imaging method is shown to estimate phase accurately over a wide range of length scales using Köhler illumination from an extended incoherent source. The method is based on estimating the longitudinal intensity derivative in the transport-of-intensity equation via convolution with multiple Savitzky-Golay differentiation filters and generalizes methods previously developed for coherent imaging to the practical scenario of partially coherent imaging. The resulting noise and resolution performance are evaluated via numerical simulation and demonstrated experimentally using a blazed transmission grating as well as a single-mode fiber as test objects.