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# Directional Derivative

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

 (1) (2)

where is called "nabla" or "del" and denotes a unit vector.

The directional derivative is also often written in the notation

 (3) (4)

where denotes a unit vector in any given direction and denotes a partial derivative.

Let be a unit vector in Cartesian coordinates, so

 (5)

then

 (6)

## See also

Derivative, Gradient, Vector Derivative

## References

Kaplan, 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.

## Referenced on Wolfram|Alpha

Directional Derivative

## Cite this as:

Weisstein, Eric W. "Directional Derivative." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DirectionalDerivative.html