Originally Posted by Antenna Guy
Just a guess, but : ?

Nope. That can't work because the lefthand side is a scalar quantity, while the righthand side is a vector.
Originally Posted by Antenna Guy
[addendeum: or is it ?]
Regards,
Bill

Not this either. Perhaps it will be simpler if I just state the result and leave the proof as an exercise. Given an orientable Riemannian manifold
, one has a preferred idea of a connection in the form of the LeviCivita connection. This allows one to define, for example, a straightforward notion of covariant differentiation on tensor fields over
. The relationship between the covariant divergence of a vector and the partial derivative of the vector is given by