In light of incessant quest of better propulsion performance, it would be opportune to probe some propulsion insights for jet engine (JE) from a power point of view. In this study, we endeavor to prescribe logic reasoning process for obtaining the JE total kinetic power and prove its degenerated counterpart. With the Lagrangian Reynolds transport approach, we also rigorously derive the highly generalized equation for this power. Moreover, the validity, significance, and importance of this novel generalized power equation are delicately demonstrated by an interesting spring/mass model with known total kinetic power. Notably, the JE total kinetic power equations are quite reasonable physically speaking, since all the velocity quantities involved are of relative nature; otherwise, the JE total kinetic power may violate the energy conservation law under certain conditions. This total kinetic power produced by jet engine involves a few more physical effects including vehicle acceleration, relative flow velocity/steadiness, inlet/exit pressures, and gravity, thus open an original route for more efficient propulsion design.