# Taking the time derivative of a curl

Is the time derivative of a curl commutative? I think I may have answered this question.... Only the partial time derivative of a curl is commutative? The total time derivative is not, since for example in cartesian coordinates, x,y,and z can themselves be functions of time. In spherical and cylindrical coordinates, even the unit vectors depend on time? Also the partial derivative of a curl in curvilinear coordinates is commutative?