Explanation of divergence in cylindrical coordinates - where does the formula come from?

In Cartesian (XYZ) coordinates, we have the formula for divergence - which is the usual definition. In cylindrical coords (rho-theta-z OR r-phi-z etc.) there is a formula for divergence too, and it's not immediately obvious how it's the same.

This video shows how to work it out.

I don't explain every single thing that happens, and I don't define any of the symbols or operators, but everything that's left out can be worked out intuitively. If you have trouble following, then read a first year calculus textbook.

This video is also motivation for studying differential forms.

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