The convective derivative is a derivative taken with respect to a moving coordinate system. It is also called the advective derivative,
derivative following the motion, hydrodynamic derivative, Lagrangian derivative,
material derivative, particle derivative, substantial derivative, substantive derivative
(Tritton 1989), Stokes derivative (Kaplan 1991, pp. 189-191), or total derivative.
It is given by

where
is the gradient operator and is the velocity of the fluid.
This type of derivative is especially useful in the study of fluid mechanics. When
applied to ,