The divergence of a continuously differentiable tensor field $\underline{\underline{\epsilon}}$ is:
$\overrightarrow{\operatorname{div}}\,(\mathbf{\underline{\underline{\epsilon}}}) = \begin{bmatrix} \frac{\partial \epsilon_{xx}}{\partial x} +\frac{\partial \epsilon_{xy}}{\partial y} +\frac{\partial \epsilon_{xz}}{\partial z} \\ \frac{\partial \epsilon_{yx}}{\partial x} +\frac{\partial \epsilon_{yy}}{\partial y} +\frac{\partial \epsilon_{yz}}{\partial z} \\ \frac{\partial \epsilon_{zx}}{\partial x} +\frac{\partial \epsilon_{zy}}{\partial y} +\frac{\partial \epsilon_{zz}}{\partial z} \end{bmatrix} $
How do you get this formula from the definition of divergence? Either formally, or with some abuse of notation?