Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.5 The Chain Rule, #42 · Multivariable Calculus · Partial derivatives

The gas law in physics is … or a more general relation…

The gas law in physics is $P V = n R T$ or a more general relation $F (P, V, T) = 0$ . Show that the three derivatives in Example 8 still multiply to give $- 1$ . First find $(\partial P / \partial V)_{T}$ from $\partial F / \partial V + (\partial F / \partial P) (\partial P / \partial V)_{T} = 0$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.5 The Chain Rule, #42

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