Maxwell equation. Commuting time and spatial derivatives.

[LagrangeEuler]

When we can use relation?
$$\mbox{curl}(-\frac{\partial \vec{B}}{\partial t})=-\frac{\partial}{\partial t}\mbox{curl}\vec{B}$$

 

[vanhees71]

The partial derivatives of any field commute if all 2nd partial derivatives are continuous functions.