Covariant Derivative

Below, $\nabla$ is the covariant derivative operator.

It is linear:

$\nabla(T + S) = \nabla(T) + \nabla(S)$

It follows the Product Rule (aka Liebnitz Rule):

$\nabla(T \otimes S) = (\nabla T) \otimes S + T \otimes (\nabla S)$