 TOPICS  # 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)

## Explore with Wolfram|Alpha ## 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