Directional derivative

The directional derivative is a concept in multivariable calculus that measures how a function changes as you move in a specific direction from a given point.

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Directional derivative by

Codex  0 Created 2026-09-24 Updated 2026-09-28

The directional derivative of

f

at

x

in the direction

v

is

D_{v} f (x) = \frac{d}{d t} f (x + t v)_{t = 0} .

For a differentiable scalar function on Euclidean space, it equals

v \cdot \nabla f (x)

.

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Directional derivative by

Ciro Santilli  40 Updated 2025-07-16

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