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Directional derivative

Calculus · Formula · Not yet linked from a lesson

Duf=∇f⋅uD_{\mathbf{u}} f = \nabla f \cdot \mathbf{u}

How fast a function changes if you walk in one chosen direction. It is largest when that direction lines up with the gradient, which is the proof that the gradient really is the steepest way up.

Symbols

u\mathbf{u}
A unit vector giving the direction of travel.
∇f\nabla f
The gradient at the current point.
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