If a frog use cutaneous respiration and lung respiration (say it is partially submerged under water), whose oxygen diffusion rate is greater and why?

The answer is Cutaneous Respiration.  It is respiration through the surface of the skin.  Cutaneous Respiration is used to supplement respiration alongside the use of their lungs. Cutaneous respiration occurs primarily as a means of carbon dioxide exchange, with the majority of oxygen exchange occurring in the lungs. Frogs take up most of their oxygen through cutaneous respiration, even if they possess lungs.