Note that the gradient of a vector is a special case of the covariant derivative, the operation results in second rank tensors;[1] except in Cartesian coordinates, it is important to understand that this is not simply an element by element gradient. Rearranging and recognizing that u ⋅ ∇ρ + ρ∇ ⋅ u = ∇ ⋅ (ρu):