The directional derivative is the rate at which the function changes at a point in the direction . It is a vector form of the usual derivative,
and can be defined as
is called "nabla" or "del"
denotes a unit vector.
The directional derivative is also often written in the notation
denotes a unit vector in any given direction and
denotes a partial derivative.
be a unit vector in Cartesian
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ReferencesKaplan, W. "The Directional Derivative." §2.14 in Advanced
Calculus, 4th ed. Reading, MA: Addison-Wesley, pp. 135-138, 1991.Morse,
P. M. and Feshbach, H. "Directional Derivatives." In Methods
of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 32-33, 1953.
on Wolfram|AlphaDirectional Derivative
Cite this as:
Weisstein, Eric W. "Directional Derivative."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DirectionalDerivative.html