Euler’s reciprocity relation

When we apply Euler s reciprocity relation to obtain the total differential of entropy by using Equation (176) for a constant interfacial flat boundary area, A, between them, we have... 

As discussed earlier, mixed second derivatives of well-behaved functions are independent of the order of differentiation. This leads to Euler s reciprocity relation... 

We now derive the Maxwell relations. These are relationships between partial derivatives that follow from Euler s reciprocal relation. Equation (5.39) (page 75). 

Euler s reciprocity relation states that the two mixed second partial derivatives of a differentiable function must be equal to each other ... 

Show that the three pairs of mixed partial derivatives that can be obtained from the derivatives in Eq. (1.2-7) conform to Euler s reciprocity relation. 

Euler s Reciprocity Relation. A second derivative is the derivative of a first derivative. If / is a differentiable function of two independent variables, x and y, there are four second derivatives ... 

Using Ihe Euler s chain relation and the reciprocal identity [Further information 2,2]... 

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