Below is part of derivation of the boltzmann equation in an electric and magnetic field. I don't understand how to arrive at the bottom equation though. It is known that the dependence of the original distribution function is the given. My idea is to use chain rule but I don't see how to get a derivative of only ε.
ashcroft and mermin? The chain rule sounds like the right idea. Multiply df0/dk by dk/dE to get df0/dE. I believe the dk/dE is proportional to 1/Vk; it needs a mass constant and hbar somewhere. Similar procedure goes for df0/dr.