Show that the power rule for derivatives applies to

Question

Question: 1. Show that the power rule for derivatives applies to rational powers of the form y = x^m/n by raising both sides to the n^th power and using implicit differentiation.

2. For constants a, b, n, R, Van der Waal's equation relates the pressure, P, to the volume, V, of a fixed quantity of a gas at constant temperature T:

(P + (n²a/V²) (V - nb) = nRT

Find the rate of change of volume with pressure, dV /dP.