Two points.

1. Math. I think you may be conflating growth rates (relative rates of change over time) with the time derivative. We are using the former (with the qualification that this works only in continuous analysis).

2. Causality. The following equation is true by definition:

Profit = L * (Profit/V) * (V/Q) * (Q/L)
Profit = L * K * P * A

However, it does not follow that because this equation is a tautology, profit “depends only on itself” as you claim. A change in one component on the right does NOT imply a compensating change in another component on the right, so as to leave profit unchanged.

Take for instance the profits of the oil companies.

Suppose today the price P rises by 10%.

This price change does not imply a change in employment L, or a change in output per employee A.

If the cost of production rose at the same rate as P – i.e. 10% – the markup K will stay the same, leading to a 10% increase in profit. (In practice, the price of oil tends to rise and fall faster than the cost of producing it, a pattern that causes P and K in the oil business to be positively correlated. This situation means that as P rises so does K, leading to an eveb faster rise in Profit.)

See footnote 42 on page 305 in Bichler, Shimshon, and Jonathan Nitzan. 2004. “Dominant Capital and the New Wars.” Journal of World-Systems Research 10 (2, August): 255-327. http://bnarchives.yorku.ca/archive/00000001/