Taking the derivative of the van der waals equation

[Razael]

Homework Statement

I'm trying to find dT/dVm for the van der waals equation. I was looking at http://courses.washington.edu/bhrchem/c456/vdw_jtc.pdf" page, but I'm confused about how they reached their result:

The Attempt at a Solution

I honestly have no idea what they did. dT/dVm of RT(Vm-b) is obviously -RT/(Vm-b)^2, and dT/dVm of -a/Vm^2 is 2a/Vm^3, and dT/dVm of P is 0, but I have no idea where [R/(Vm-b)](dT/dVm) came from. Am I missing something obvious here? It's been a while since calc.

 

[Fredrik]

The first term is the product of RT and 1/(V_m-b), so you need to use the product rule: (fg)'(x)=f'(x)g(x)+f(x)g'(x).