There are various gas laws in addition to the well$-$known ideal gas law and the van der Waals gas law that we learned from CHEM$1070.$ Here is another example by Clausius:

$[P+\frac{a{n}^2}{(VT{)}^2}](V-nb)=nRT$

where $a,b$ are constants specific to the gas, and the other symbols carry the same meanings as those in the ideal gas law.

a$)$ Compute $\frac{dP}{dT}.$ Assume any variables other than $P$ and $T$ are constants. Such a derivative is more accurately called a partial derivative and is labeled as $\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{T}}$ or $(\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{T}}{)}_{n,V}$

b$)$ Compute $\frac{dP}{dV}.$ Assume any variables other than $P$ and $V$ are constant.

c$)$ Compute $\frac{dP}{dn}.$ Assume any variables other than $P$ and $n$ are constant.