When x, y, and z are related by an equation F(x, y, z) = 0, we sometimes write (∂z/∂x)_y in place of ∂z/∂x to indicate that in the differentiation, z is treated as a function of x with y held constant (and similarly for the other variables).

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(a) Use Eq. (7) to prove the cyclic relation dy (2x), (2), (3/2). - y = -1 (b) Verify Eq. (10) for F(x, y, z) = x + y + z = 0. (c) Verify the cyclic relation for the variables P, V,T in the Ideal Gas Law PV = nRT = 0 (n and R are constants).