MathPlotAI Logo MathPlotAI

Geometric Proof of Derivative of Arctan

Geometric Proof of Derivative of Arctan
Loading the math board and drawing, please wait…
2016-12-29 00:48
CircleAngleCalculusDerivativeGeometric Construction
This example demonstrates the derivative of the arctan function using geometric methods. Key math concepts include derivatives, slope, circles, angles, and geometric transformations. Construction highlights the use of GeoGebra commands such as Intersect, Segment, Circle, Ray, Angle, Midpoint, Rotate, OrthogonalLine, CircleArc, Center, Polygon, and Point. Suitable for high school and above learning calculus and geometric constructions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Intersect(c, f, 1) → A
  3. Segment(O, F) → l
  4. Circle((0, 0), l) → d
  5. Intersect(d, f, 1) → D
  6. Segment(O, A) → g
  7. Segment(O, D) → h
  8. Ray(O, A) → i
  9. Intersect(d, i, 1) → C
  10. Intersect(c, h, 1) → B_1
  11. Segment(A, C) → j
  12. Intersect(f, xAxis) → B
  13. Angle(A, O, B_1) → θ
  14. Segment(A, O) → m
  15. Segment(O, D) → n
  16. Midpoint(m) → G
  17. Midpoint(n) → H
  18. Rotate(H, π / 5, O) → H'
  19. Segment(A, B) → s
  20. Segment(O, B) → f_1
  21. Segment(D, B) → g_1
  22. Angle(B, O, D) → α
  23. Angle(B, O, A) → β
  24. Segment(O, A) → h_1
  25. Segment(O, D) → i_1
  26. Segment(D, C) → p
  27. Segment(A, C) → a
  28. Segment(A, D) → e
  29. Midpoint(p) → I
  30. Midpoint(j) → J
  31. Segment(D, J) → j_1
  32. Segment(A, I) → k_1
  33. Intersect(j_1, k_1) → K
  34. OrthogonalLine(C, j) → l_1
  35. Angle(A, B, O) → γ
  36. Angle(O, A, B) → δ
  37. Angle(C, A, D) → ε
  38. Intersect(l_1, yAxis) → M
  39. Angle(A, C, M) → ζ
  40. CircleArc(O, C, D) → c_1
  41. Segment(O, C) → m_1
  42. Midpoint(m_1) → L
  43. Center(c_1) → N
  44. Rotate(C, θ / 2, O) → C'
  45. Polygon(O, D, B) → poly1, b_2, o_1, d_1
  46. Point(xAxis) → E
  47. Point(xAxis) → P
  48. Point(p_1) → Q
  49. OrthogonalLine(Q, p_1) → q_1
  50. OrthogonalLine(E, q_1) → r_1
  51. Intersect(q_1, r_1) → R
  52. Point(s_1) → U
  53. Segment(S, U) → e_1
  54. OrthogonalLine(U, e_1) → f_2
  55. OrthogonalLine(T, f_2) → g_2
  56. OrthogonalLine(S, g_2) → h_2
  57. Point(h_2) → V
  58. Point(g_2) → W
  59. Polygon(S, U, W, V) → poly2, s_2, u_1, w_1, v_1
  60. Point(n_1) → Z
  61. Ray(Z, C) → j_2
  62. Intersect(l_1, k_2) → A_1
  63. Intersect(l_1, l_2) → C_1
  64. Segment(A_1, C_1) → n_2