Partial Derivative Demo by Enoch Bentley

Partial Derivative Demo by Enoch Bentley
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2016-02-25 23:45
This example demonstrates the concept of partial derivatives in three-dimensional space, visually representing the geometric meaning of partial derivatives through dynamic graphics. Key math concepts include partial derivatives, 3D vectors, coordinate systems, function graphs, and linear representations. GeoGebra commands and objects like Textfield, Derivative, Point, CurveCartesian, Line, and Segment are used to construct the function graph and its derivative lines. Suitable for high school and above learners to understand the intuitive meaning and calculation methods of partial derivatives.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox1
  2. Derivative(f(x, y), x) → dfx
  3. Derivative(f(x, y), y) → dfy
  4. Point(a) → A
  5. CurveCartesian(t, y(A), g(t), t, -10, 10) → c
  6. Point(e) → B
  7. Line((x(B), y(A), f(x(B), y(A))), Vector[(1, 0, dfx(x(B), y(A)))]) → h
  8. CurveCartesian(x(B), t, g2(t), t, -10, 10) → k
  9. Line(P, Vector[(0, 1, dfy(x(B), y(A)))]) → l
  10. Segment(A, XYP) → m
  11. Segment(B, XYP) → n
  12. Segment(P, XYP) → p