Directional Derivatives Interactive Demonstration

This GeoGebra example demonstrates the concept of directional derivatives, which is the rate of change of a function in a specific direction. It visually shows the function graph, direction vector, and tangent slope to illustrate the geometric meaning. Core math concepts include derivatives, directional derivatives, partial derivatives, gradient vectors, cosine functions (for direction cosines), conic sections, logarithmic functions, sequences and series, and perimeter calculations. In terms of construction, it uses commands like Textfield for text input, Segment for drawing lines, Circle for circles, Point for points, Vector for direction vectors, IntegralBetween for integral areas, Tangent for tangents, Slope for slopes, CurveCartesian for Cartesian curves, and Plane for planes. Objects such as point A, function f, input box, point P, parameters a and c, points B and u, C and D with distance d, E and e, height h, functions g and i, F and j, k, directional derivative function duf, G and l, text, parameters b, p, m, n are used to create an interactive environment. It is suitable for university calculus, multivariable function analysis, or related math courses for teaching and self-study.