/sci/ - Science & Math

I think I get the intuitive idea of the material derivative, and I get how the definition is derived from the chain rule. But I don't get the final step in this derivation of the "balance in momentum equation" (see pic related).
The RHS of equation (BM1) is simply the total forces acting on a parcel of liquid, but on the LHS, why is the acceleration the material derivative of u (Du/Dt) and NOT just the regular derivative (du/dt)?

At time t, if I am concentrating on the force acting at point (x, y, z), then I am concerned with the acceleration of the fluid at point (x,y, z) at time t, and how is that not just du / dt?