(1)

and D/dt is called particle differentiation, because it follows the rate of change of a particle as it leaves the point x, y, z; but

dF/dt, dF/dx, dF/dy, dF/dz

(2)

represent the rate of change of F at the time t, at the point, x, y, z, fixed in space.

The components of acceleration of a particle of fluid are consequently

Du= du+ u du+ v du+ w du,
dt dtdx dydz

(3)

Dv= dv+ u dv+ v dv+ w dv,
dt dtdx dydz