Mathematically, the divergence is noted by:
∇·F
Where F is the vector field that the divergence operator is being applied to. Expanded, the notation looks like this:
∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z
if F = [Fx, Fy, Fz]
A closer examination of the pattern in the expanded divergence reveals that it can be thought of as being like a dot product between ∇ and F if ∇ was:
[∂/∂x, ∂/∂y, ∂/∂z]
and its components were thought to apply their respective derivatives to whatever they are multiplied by.