I'd like to use 2-d for simplification. Divergence is the rate of change of a component of a field F as you travel along that component's direction. So Fx represents the part of F flowing the X direction and same with Fy along the Y direction, and so divergence is calculated by dFx/dx + dFy/dy. But isn't it possible that flow of Fx, or flow of F in the X direction, changes not as a function of X, but as a function of Y? So as you travel along the X axis at a constant Y, the change of Fx is 0. And likewise with Fy: it's possible that the flow of Fy changes as a function of the X direction and so the change of Fy along the Y axis is 0. Given this, we get that total divergence is dFx/dx + dFy/dy = 0 + 0 = 0, meaning there is no flow out of the surface. But it seems to me that there must be some flow out of the surface, it's just that the rate changes as you move about a different axis. So shouldn't divergence actually be adding up how Fx changes as you move along both the X and Y axis, and how Fy changes as you move along X and Y axis?