Maybe I am just really tired, but I understand for output per worker in Cobb Douglas, it is Y/P=T*K/L, can it be transformed to TFP%+%K/L=%Y/P say: Country A’s labor productivity grew by 2.4% per year, of which 0.6% came from TFP growth and 1.8% from capital deepening (2.4% – 0.6% = 1.8%).
Yes that transformation is due to partial differentiation (mathematically speaking).
so delta Y/P = Delta T + Delta K/L
where delta X = Change in variable X…