Photometric stereo leverages variations in illumination conditions to reconstruct surface normals.Display photometric stereo, which employs a conventional monitor as an illumination source, has the potential to overcome limitations often encountered in bulky and difficult-to-use conventional setups. In this paper, we present differentiable display photometric stereo (DDPS), addressing an often overlooked challenge in display photometric stereo: the design of display patterns. Departing from using heuristic display patterns, DDPS learns the display patterns that yield accurate normal reconstruction for a target system in an end-to-end manner.To this end, we propose a differentiable framework that couples basis-illumination image formation with analytic photometric-stereo reconstruction. The differentiable framework facilitates the effective learning of display patterns via auto-differentiation.Also, for training supervision, we propose to use 3D printing for creating a real-world training dataset, enabling accurate reconstruction on the target real-world setup.Finally, we exploit that conventional LCD monitors emit polarized light, which allows for the optical separation of diffuse and specular reflections when combined with a polarization camera, leading to accurate normal reconstruction.Extensive evaluation of DDPS shows improved normal-reconstruction accuracy compared to heuristic patterns and demonstrates compelling properties such as robustness to pattern initialization, calibration errors, and simplifications in image formation and reconstruction.