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Click on the left plot to place a point. The line through the point in the direction û is shown, and the 1D slice f along that line is plotted on the right.

Use the θ slider at the top to change the direction û.

Toggle options in the sidebar to show the heat map, level sets, gradient vector, or 3D surface.

You can enter custom functions in the text box.

Overview

The directional derivative D_ûf measures the rate of change of f at a point in the direction of a unit vector û.

D_ûf(r₀) = ∇f(r₀) · û

Here ∇f is the gradient vector, and û = (cos θ, sin θ).

The right-hand plot shows f restricted to the line through r₀ in the direction û, parameterised by arc length s. The slope of this 1D curve at s = 0 is exactly D_ûf.

When ∇f is displayed, the projection of ∇f onto û gives the directional derivative geometrically.