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Partial and Directional Derivatives Demo

Partial and Directional Derivatives Demo
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2019-11-23 06:05
VectorCalculusDerivative
This example demonstrates the geometric meaning of partial and directional derivatives in 3D space, showing the relationship between derivatives, tangent planes, and direction vectors through interactive dynamics; core math concepts include partial derivatives, directional derivatives, gradient, tangent planes, and vector operations; construction highlights use of GeoGebra commands/objects like Textfield, IntersectPath, Derivative, Line, Vector, OrthogonalPlane for dynamic function plotting, tangent lines, and vector/plane visualization; suitable for university calculus and linear algebra teaching/learning to grasp key ideas of multivariable differential calculus.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox1
  2. IntersectPath(p, f) → eq1
  3. Derivative(f, x) → f_{x}
  4. Line(A, Vector[(1, 0, f_{x}(a, b))]) → g
  5. Derivative(f, y) → f_{y}
  6. Line(A, Vector[(0, 1, f_{y}(a, b))]) → h
  7. IntersectPath(q, f) → eq2
  8. Line(A, Vector[(1, 0, f_{x}(a, b))]) → i
  9. Vector((u1, u2)) → u
  10. OrthogonalPlane(A, Vector[u ⊗ Vector[(0, 0, 1)]]) → r
  11. IntersectPath(r, f) → eq3
  12. Line(A, Vector[(u1, u2, (f_{x}(a, b) * u1) + (f_{y}(a, b) * u2))]) → j

AI Drawing Prompt Reference

Visualize a function in 3D space, demonstrating the geometric meaning of partial and directional derivatives. Plot the function curve and mark the tangent lines at point A using the partial derivative vectors. Then, draw an orthogonal plane at point A using a direction vector u, showing how it intersects the function curve. Highlight the directional derivative vector and illustrate the relationship between derivatives, tangent planes, and direction vectors through interactive dynamics to grasp key multivariable calculus concepts.
The prompt above was compiled from the original drawing commands and is for reference only.