Maxwell's equations are statements of experimental results in differential form, plus Maxwell's guess that there are no magnetic monopoles and that there is a displacement current to carry current through a capacitor, providing continuity.
You don't really derive them (unless the professor had in mind, "Produce them from the integral forms"). A better question would be, "Derive the EM wave equation in free space from Maxwell's equation and determine the phase velocity."
Pretty much what he was looking for. Keep in mind that this was at the end of a course covering pretty much all of static fields. And this course was a precursor and prerequisite for the following course which was about the application and implications of Maxwell's equations.
The latter was taught by my favorite professor, who seemed to have a radar to know when the class was not following. Without request, he would erase what he had written on the board and restart.
The lab was fun. Three quarters of the way through the first 2-hour lab, he said "By the way, anyone who gets the right answer loses points on this exercise. The point is to teach you how hard it is to come to the right answer."
He told a story of his work during WW II. His favorite thing then was to build a little $50 piece of equipment to render million-dollar radar sets useless. Clearly his task was to help improve the radar set. "The odds are stacked in favor of the jammer." Who obviously cheer for the inverse of the distance to the fourth power.
