It seems if I call the LHS F as follows:

F(P1,P2,Q) = P1 - P2 - k * ( f(P1,Q) + g(P2,Q) )

Then partial derivs:

dQ/dP1 = ( dF/P1 ) / (dF /dQ )

dQ/dP2 = ( dF/P2 ) / (dF /dQ )

Is that correct? If so then how do extend it 2 two functions, F and G:

F(P1,P2,P3,Q) = P1 - P2 - k1 * ( f(P1,Q) + g(P2,Q) ) = 0

G(P1,P2,P3,Q) = P2 - P3 - k2 * ( g(P2,Q) + h(P3,Q) ) = 0

( where P2 and Q are the 2 variables to be solved for in the 2 simultaneous equations )

To find partial derivs:

dQ/dP1, dQ/dP3

?