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Partial Derivatives Demonstration

Partial Derivatives Demonstration
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2022-05-20 12:19
Coordinate GeometryCalculusDerivative
This example demonstrates the concept of partial derivatives. It uses various GeoGebra commands such as Segment, Textfield, Derivative, etc., to construct a dynamic partial derivative graph. Suitable for students and teachers in calculus courses.

GeoGebra Commands & Parameters

  1. Segment(A, B) → g
  2. Textfield(f) → InputBox1
  3. Derivative(f, x) → fx
  4. Derivative(f, y) → fy
  5. CurveCartesian(x(A), s, f(x(A), s), s, -10, 10) → cy
  6. CurveCartesian(s, y(A), f(s, y(A)), s, -10, 10) → cx
  7. CurveCartesian(x(A) + s, y(A), f(x(A), y(A)) + (s * fx(x(A), y(A))), s, -10, 10) → tx
  8. CurveCartesian(x(A), y(A) + s, f(x(A), y(A)) + (s * fy(x(A), y(A))), s, -10, 10) → ty
  9. Textfield(Ax) → InputBox2
  10. Textfield(Ay) → InputBox3
  11. Function(f(x(A), y(A)) + (fx(x(A), y(A)) * (x - x(A))) + (fy(x(A), y(A)) * (y - y(A))), x(A) - 1, x(A) + 1, y(A) - 1, y(A) + 1) → TangP
  12. Point(zAxis) → D
  13. Intersect(zAxis, yAxis) → E
  14. Vector(D, E) → u
  15. Point(xAxis) → F
  16. Vector(F, E) → v
  17. Point(yAxis) → G
  18. Intersect(yAxis, zAxis) → H
  19. Vector(G, H) → w
  20. Element(list1, faces) → Selectedvector

AI Drawing Prompt Reference

Draw a graph showing the partial derivatives of a function, including the function surface, x, y, and z axes, and the tangent plane and line at point A. First, draw the x and y axes, then plot the surface based on the function expression. Next, select a point A on the surface and draw the partial derivative tangent line and plane at point A. Finally, draw the z axis and select a point D on the z axis, with intersection point E on the y axis, and points F and G on the x and y axes respectively, to draw vectors u, v, and w.
The prompt above was compiled from the original drawing commands and is for reference only.