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Directional Derivative Demo by Andreas Lindner

Directional Derivative Demo by Andreas Lindner
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2017-06-16 20:31
VectorCalculusDerivative
This example demonstrates the calculation and visualization of directional derivatives of a function at a point in space along any direction. Key math concepts include directional derivatives, gradients, vectors, and 3D coordinate systems. Construction highlights involve commands like OrthogonalLine, Derivative, Segment, Plane, Intersect, Polygon, Angle, Textfield, Line, and Vector to build function graphs, gradient vectors, directional vectors, and geometric representations of directional derivatives. Suitable for university calculus and linear algebra teaching demonstrations or student exploration.

GeoGebra Commands & Parameters

  1. OrthogonalLine(Q', xOyPlane) → j
  2. Derivative(f, x) → f_x
  3. Derivative(f, y) → f_y
  4. Segment(P_2, P_1) → t_x
  5. Segment(P_3, P_4) → t_y
  6. Plane(t_x, t_y) → b
  7. Intersect(j, b) → C
  8. Segment(P', P) → s
  9. Polygon(P, P_1, P_5) → Vieleck1, p_2, p_3, p_1
  10. Polygon(P, P_6, P_3) → Vieleck2, p_4, p_6, p_5
  11. Angle(P_3, P_6, P) → α
  12. Angle(P_1, P_5, P) → β
  13. Polygon(P_7, P_8, P_9, P_{10}) → Vieleck3, p_7, p_8, p_9, p_{10}
  14. Textfield(f) → Textfeld1
  15. Line(P, C) → d
  16. Vector(P', Q') → r
  17. Vector(P', P' + (k_x, k_y)) → gradf
  18. Segment(F, C) → k
  19. Intersect(p_1, t_y) → A
  20. Segment(A, F) → l
  21. Intersect(p_1, l) → B
  22. Plane(P', Q', A) → a