A vector derivative is a derivative taken with respect to a vector field. Vector derivatives are extremely important in physics, where they arise
throughout fluid mechanics, electricity and magnetism, elasticity, and many other
areas of theoretical and applied physics.

The following table summarizes the names and notations for various vector derivatives.

Gradshteyn, I. S. and Ryzhik, I. M. "Vector Field Theorem." Ch. 10 in Tables
of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press,
pp. 1081-1092, 2000.Morse, P. M. and Feshbach, H. "The
Differential Operator " and "Table of Useful Vector and Dyadic Equations."
In Methods
of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 31-44, 50-54,
and 114-115, 1953.