Partial Derivatives Demo

Partial Derivatives Demo
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2018-01-12 01:47
This example demonstrates the geometric meaning of partial derivatives dfx and dfy of a 3D function f in space, showing how moving point A on the surface illustrates these concepts. Core math concepts include partial derivatives, directional derivatives, 3D function graphs, and analytical geometry. GeoGebra commands used are PointIn, Derivative, Line, Textfield, involving objects like point A, function f, partial derivatives dfx/dfy, and sliders b/c. Suitable for university calculus and mathematics education visualization.

GeoGebra Commands & Parameters

  1. PointIn(f) → A
  2. Derivative(f(x, y), x) → dfx
  3. Derivative(f(x, y), y) → dfy
  4. Line(A, Vector[(1, 0, dfx(x(A), y(A)))]) → f_1
  5. Line(A, Vector[(0, 1, dfy(x(A), y(A)))]) → g
  6. Line(A, Vector[(1, 0, dfx(x(A), y(A))) + (0, 1, dfy(x(A), y(A)))]) → h
  7. Textfield(f) → InputBox1