Differential thrust can be used for directional control on distributed electric propulsion aircraft. This paper presents an assessment of flight dynamics and control under engine inoperative conditions at minimum control speed for a typical distributed propulsion aircraft employing differential thrust. A methodology consisting of an aerodynamic data acquisition module and a non-linear six-degrees-of-freedom flight dynamics model is proposed. Directional control is achieved using a controller to generate a yaw command, which is distributed to the propulsors through a thrust mapping approach. A modified version of the NASA X-57 aircraft is selected for case studies, where the engine inoperative condition is considered to impact the three leftmost propulsors during climb at minimum control speed. The objective also includes the assessment of the impact of the aero-propulsive coupling for such an aircraft during a failure case. Results show that during the recovery manoeuvre, the aircraft experiences a 78% reduction in total thrust and 30% reduction in total lift caused by the aggressive yaw control effort required to control the heading of the aircraft. Consequently, the powered-stall speed is increased, and the aircraft temporarily loses altitude during the recovery manoeuvre. Differential thrust provides sufficient yaw authority during the engine inoperative condition, and is, therefore, seen to potentially replace the functionality of the rudder for the climb condition that was studied. Additionally, reduction of the vertical tail area was explored and seen to be possible if the response time of the system is low enough. For the studied configuration, this required a response within 400 ms for reduced vertical tail areas.