A derivative taken with respect to a moving coordinate system, also called the Lagrangian derivative, substantive derivative (Tritton 1989), or Stokes derivative (Kaplan 1991, pp. 189-191). 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 ,

Batchelor, G. K. An Introduction to Fluid Dynamics. Cambridge, England: Cambridge University Press, p. 73, 1977.

Kaplan, W. Advanced Calculus, 4th ed. Reading, MA: Addison-Wesley, 1991.

Tritton, D. J. "The Substantive Derivative." §5.5 in Physical Fluid Dynamics, 2nd ed. Oxford, England: Clarendon Press, pp. 53-55, 1989.

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Weisstein, Eric W. "Convective Derivative." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ConvectiveDerivative.html