It's a straight mathematical relationship, irrespective of jet/piston. Differentiate the drag equation (split into zero-lift and lift induced drag) with respect to velocity and set to zero to get the minumum. Then do the same for power (drag x velocity). Solve the 2 equations simultaneously and the speed ratio pops out. You can use the same method to derive range speed for a jet aircraft.
My excuse for not doing it here is that I can't get all of the symbols I need!
QED