Question

If gas in a cylinder is maintained at a constant temperature T, the pressure P is related to the volume V by a formula of the form P = ((nRT)/(V-nb))-((an^2)/(V^2)), in which a, b, n, and R are constants. Find dP/dV.

Answer 1

One thing that might help is to condense the constant expressions into easier to see pieces.
e.g. let nRT=w, nb=z, an^2=k
Then your function becomes
\(\large P(V)=\frac{wV^2-kV+kz}{V^3-zV^2}\)

Then you can use quotient rule to find the derivative.