## Thomas' Calculus 13th Edition

$P_n=\frac{RT}{V}$ $P_R=\frac{nT}{V}$ $P_T=\frac{nR}{V}$ $P_V=\frac{-nRT}{V^2}$
Take the first partial derivatives of the given function. When taking partial derivative with respect to n, treat R, T, and V as constants. Use the same method when taking partial derivative with respect to R, T, and V: $P_n=\frac{1RT}{V}=\frac{RT}{V}$ $P_R=\frac{n1T}{V}=\frac{nT}{V}$ $P_T=\frac{nR1}{V}=\frac{nR}{V}$ $P_V=\frac{-nRT}{V^2}$