The nuclear gradient expression can be readily used in any MQC simulations, such as Ehrenfest and FSSH approaches demonstrated in this work, as well as nuclear wavepacket approaches that require nuclear gradient. The theoretical developments in this work could significantly benefit the polariton quantum dynamics community with a rigorous nuclear gradient of the moleculecavity hybrid system and could have a broad impact on the future non-adiabatic simulations of polariton quantum dynamics.