The so-called increase rate of elevation angle is the change rate of elevation angle to time, that is, da/dt.

But at first we didn't get an explicit a = f(t), but an implicit solution similar to f(a) = g(t), so we can use the derivative rule of implicit function without solving the explicit solution. (In fact, many formulas cannot be solved explicitly, but it is very simple here. )

The derivation rule of implicit function is the above solution process. It is no coincidence that it is often used in advanced mathematics.