A sufficient condition for equal second-order partial guidance

The problem that has plagued me for so many years has finally been solved: Why is my grandfather's father and father's grandfather the same person, while my grandmother's mother and mother's grandmother are not the same person?

Answer: the premise that the order of the second-order partial direction does not affect the result is that the derivative is continuous in the interval.

 

[I have read it before, but it is not saved]

A sufficient condition for equal second-order partial guidance