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Directional Derivative by jesseburke

Directional Derivative by jesseburke
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2020-05-13 22:30
VectorCalculusDerivative
This example illustrates the concept of directional derivative. Using vector and derivative methods in coordinate geometry, it shows the rate of change of a function at a point in a specific direction. GeoGebra commands such as NDerivative, UnitVector, and Vector are used in the construction. Suitable for university calculus courses.

GeoGebra Commands & Parameters

  1. NDerivative(A, x) → parx
  2. NDerivative(A, y) → pary
  3. UnitVector(Vector[P, (x0 + 1, y0, A(x0, y0) + parx(x0, y0))]) → vx
  4. UnitVector(Vector[P, (x0, y0 + 1, A(x0, y0) + pary(x0, y0))]) → vy
  5. UnitVector(Vector[P, (x0 + cos(theta), y0 + sin(theta), A(x0, y0) + (cos(theta) * parx(x0, y0)) + (sin(theta) * pary(x0, y0)))]) → vu
  6. Vector(P0, (x0 + 1, y0, 0)) → i
  7. Vector(P0, (x0, y0 + 1, 0)) → j
  8. Vector(P0, (x0 + cos(theta), y0 + sin(theta), 0)) → u
  9. IntersectPath(r, A) → eq1