From what source do governments derive their just powers?

The answer to this question is very dependent on both the system of government (democracy? theocracy? Dictatorship?) and level of government (federal? state? municipal?) to which you are referring. But for all intents and purposes, let's say you are asking about the American government:

The Framers wrote the Constitution following the philosophy that a government derives it's power from the consent of the governed - AKA, the people. That is why our system of government is a Democratic Republic ("demos" means "people"); American citizens elect others to represent them in office. One could also say that a source of "just power" for the government is the United States Constitution itself. The Constitution is considered to be the highest source of legitimate authority. Therefore, it gives the three branches of government (executive, legislative, judicial) responsibilities and powers. For example, the Legislative Branch has the power to regulate interstate commerce because of the commerce clause (Article 1, Section 8, Clause 3).