\begin{definition}[Definition:Divergence Operator/Cartesian 3-Space]
Let $R$ be a region of Cartesian $3$-space $\R^3$.
Let $\map {\mathbf V} {x, y, z}$ be a vector field acting over $R$.
The '''divergence of $\mathbf V$''' is defined as:
{{begin-eqn}}
{{eqn | l = \operatorname {div} \mathbf V
      | o = :=
      | r = \nabla \cdot \mathbf V
}}
{{eqn | r = \dfrac {\partial V_x} {\partial x} + \dfrac {\partial V_y} {\partial y} + \dfrac {\partial V_z} {\partial z}
      | c = {{Defof|Dot Product}}
}}
{{end-eqn}}
\end{definition}