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Visualizing Partial Derivatives

Visualizing Partial Derivatives
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2020-08-15 13:20
FunctionCalculusDerivative
This example dynamically illustrates the concept of partial derivatives. It involves the calculation of partial derivatives of a function and how to visually understand the meaning of partial derivatives. The construction uses commands such as PointIn, Derivative, IntersectPath, Line, and Vector, suitable for university-level calculus courses.

GeoGebra Commands & Parameters

  1. PointIn(z = 0) → A
  2. Derivative(f, x) → Fx
  3. Derivative(f, y) → Fy
  4. IntersectPath(p, f) → eq1
  5. IntersectPath(q, f) → eq2
  6. Line(B, Vector[(1, 0, Fx(x(A), y(A)))]) → g
  7. Line(B, Vector[(0, 1, Fy(x(A), y(A)))]) → h
  8. Vector(B, B + (1, 0, Fx(x(A), y(A)))) → a
  9. Vector(B, B + (0, 1, Fy(x(A), y(A)))) → b

AI Drawing Prompt Reference

Draw a graph illustrating partial derivatives. Include a function curve, a point, and two lines emanating from the point, representing partial derivatives with respect to x and y. The lines should indicate the direction of the derivatives. The graph should clearly show the concept of partial derivatives to help understand the rate of change of a function at a specific point.
The prompt above was compiled from the original drawing commands and is for reference only.