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Directional Derivative: A Tilted Slice

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Directional derivative as the slope of a vertical slice. Pick a point on a surface z = f(x, y) and a unit direction u; the plane through that point parallel to u cuts the surface along a curve whose slope at the point is D_u f. Algebraically D_u f = ∇f · u, so every direction's slope is a projection of the gradient.

directional derivativegradientunit directionpartial derivativelevel curvesdot product
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