Vector operator expansion ∇·(c∇u) in 3D

hi
I am working on a set of coupled differential equations in the equation based modeling (3D).
Assuming that u=[u, v, w].
I am looking to evaluate the term ∇·(c∇u) to obtin the matrix c.
I was wondering if the expansion in the attached file is correct.

Please advise
Thank you,

NP