Given the generalized homogeneous function f(λθ1x1,λθ2x2,…,λθnxn)=λf(x1,…,xn), show that θ1x1(∂x1∂f)x2……xn+⋯+θnxn(∂xn∂f)x1…,xn−1=f(x1,…,xn). This result is a generalization of the Euler's theorem discussed HERMODYNAMICS, FUNDAMENTALS 27 in the text. It plays an important role in the theory of phase transitions when deriving what are known as "scaling" equations of state for systems near critical points.
