The divergence of A {\displaystyle A} , div ⁡ A = 1 det g ∂ ∂ x i ( A i det g ) , {\displaystyle \operatorname {div} A={\frac {1}{\sqrt {\det g}}}{\frac {\partial }{\partial x^{i}}}\left(A^{i}{\sqrt {\det g}}\right),} is invariant under change of coordinates.