Directional Derivative by Daniel Vallieres
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This example illustrates the concept of directional derivative, which is the rate of change of a function in a specific direction. By constructing vectors and functions, it provides a visual understanding of how to calculate directional derivatives. Utilizes Vector and Line commands, suitable for high school mathematics education.
GeoGebra Commands & Parameters
Vector((1, 1), (1 + cos(θ), 1 + sin(θ))) → uLine((1, 1, 2), (1 + cos(θ), 1 + sin(θ), 2 + (2 * cos(θ)) + (2 * sin(θ)))) → f
AI Drawing Prompt Reference
Show a point at (1,1) in the plane with a unit vector starting there, pointing at angle θ so its tip is at (1+cosθ, 1+sinθ). In 3D, mark the point (1,1,2) and draw a line through it with direction vector (cosθ, sinθ, 2cosθ+2sinθ); this line represents the tangent line giving the directional derivative of the function at that point in the chosen direction.
The prompt above was compiled from the original drawing commands and is for reference only.