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Visualizing Partial Derivatives by Andrew Cooper

Visualizing Partial Derivatives by Andrew Cooper
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2019-10-03 20:46
FunctionCalculusDerivative
This example dynamically illustrates the concept of partial derivatives. It involves the partial derivatives of multivariable functions, using tangent lines and planes to intuitively understand the meaning of partial derivatives. Commands used include PointIn, Derivative, IntersectPath, Line, and Vector. Suitable for university 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