6-9 Charge-Current Continuity Derivation

The charge current continuity equation is derived in this video. This video shows the derivation starting from first principles and applying relevant vector calculus transformations. The charge-current continuity relation is also called the charge continuity equation.

I am teaching using the Fawwaz T. Ulaby textbook as a reference. This is covered in chapter 6-9 of Fundamentals of Applied Electromagnetics, 8th edition.

[yosefpatinio]

in the minute 5:20
if the volume changes, it possible to move the derivative inside the integral?
if not, why?
and how the continuity equation will be changed?