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Partial Derivatives: Dynamic Illustrator

Partial Derivatives: Dynamic Illustrator
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2017-12-28 11:19
FunctionCalculusDerivative
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources Multivariable Calculus
This example dynamically illustrates the concept of partial derivatives. It involves the core mathematical concept of partial derivatives, which are the derivatives of multivariable functions with respect to one variable. Using GeoGebra commands such as Plane, IntersectPath, Derivative, Textfield, etc., users can observe the changes in partial derivatives visually. Suitable for teaching multivariable calculus in university mathematics courses.

GeoGebra Commands & Parameters

  1. Plane((x(P), 2, 300), (x(P), 1, 100), (x(P), 1, 200)) → d
  2. IntersectPath(d, f) → e
  3. Plane(P, (100, y(P), 100), (200, y(P), 200)) → g
  4. Derivative(f, y, 1) → k
  5. Derivative(f, x, 1) → l
  6. IntersectPath(g, f) → m
  7. IntersectPath(g, n) → o
  8. IntersectPath(d, n) → t
  9. Textfield(f) → InputBox1
  10. Point(IntersectPath[g, n]) → B
  11. Sphere(B, 1) → a_1
  12. IntersectPath(b_1, a_1) → c_1
  13. Intersect(w, c_1) → C, D
  14. Sphere(D, abs(j)) → e_1
  15. Line(D, (x(D), y(D), z(D) + 1)) → f_1
  16. Intersect(f_1, e_1) → E, F
  17. Polygon(B, D, F) → t1, f_2, b_2, d_2
  18. Polygon(B, D, E) → t2, e_2, b_3, d_3
  19. Segment(D, F) → g_1
  20. Segment(D, E) → h_1
  21. Segment(B, D) → i_1
  22. Point(t) → G
  23. Line(G, (x(G), y(G) + 1, z(G))) → j_1
  24. Sphere(G, 1) → k_1
  25. Intersect(j_1, k_1) → A, H
  26. Sphere(H, abs(p)) → l_1
  27. Line(H, (x(H), y(H), z(H) + 1)) → m_1
  28. Intersect(m_1, l_1) → I, J
  29. Polygon(G, H, J) → t3, j_2, g_2, h_2
  30. Polygon(G, H, I) → t4, i_2, g_3, h_3
  31. Segment(H, J) → n_1
  32. Segment(H, I) → p_1
  33. Segment(H, G) → q_1