Urban air taxis, also known as urban air mobility (UAM) vehicles, are anticipated to be an area of significant market growth in the near future. These vehicles are typically vertical takeoff and landing (VTOL) designs which are capable of carrying 1 to 30 passengers in an intra-urban environment with flights of less than 50 nautical miles. Development of UAM vehicles and their integration into the airspace will be enabled by advancements in a number of areas including electrified propulsion systems, structures, acoustics, automation, and controls. However, the strong multidisciplinary interactions for these unique vehicles presents a significant new design challenge. This work describes the development of a multidisciplinary analysis and optimization environment which can be used to support the conceptual design of these UAM vehicles, using efficient gradient based optimization with analytic derivatives. The tools included in this multidisciplinary analysis model the aircraft trajectory, vehicle aerodynamics, structures, and electrified propulsion system. The multidisciplinary environment created in this research is unique in that all the physics tools are tightly integrated together, with the trajectory model directly calling the aerodynamics, structures, and propulsion models. This multidisciplinary analysis environment is then demonstrated in the design optimization of a turboelectric tiltwing UAM vehicle concept.