Directional Derivative: Visualizing Slope Along Any Vector

This GeoGebra example visualizes the directional derivative of a multivariable function on a 3D surface. It demonstrates that at a point A on the surface, the slope of the tangent line along a chosen direction vector u equals the directional derivative. The core mathematical concepts include partial derivatives, directional derivatives, gradients, tangent planes, and the intersection of a plane with a surface. The construction uses commands such as PointIn to place a point on the surface, Vector to define the direction u, Plane to create a vertical plane through A containing u, IntersectPath to obtain the curve g where the plane cuts the surface, and Line/Point to mark the tangent line and intersection points. By dragging the vector, learners can see how the directional derivative changes with direction. This is ideal for university-level calculus or multivariable function courses, and also serves as an intuitive introduction for advanced high school students.