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Definition of Directional Derivative

Definition of Directional Derivative
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2019-05-07 20:46
VectorCalculusDerivative
This example illustrates the definition of a directional derivative. Key concepts include directional derivatives and vectors. Using GeoGebra commands such as NDerivative, Vector, IntersectPath, etc., the geometric meaning of directional derivatives is constructed. Suitable for university-level calculus courses.

GeoGebra Commands & Parameters

  1. NDerivative(f, y) → dy
  2. NDerivative(f, x) → dx
  3. Vector(fOfA, Px) → fx
  4. Vector(fOfA, Py) → fy
  5. Vector(A, (a + 1, b, 0)) → i
  6. Vector(A, (a, b + 1, 0)) → j
  7. Vector(A, A1) → u
  8. OrthogonalPlane(fOfA, Vector[fx ⊗ fy]) → tangentPlane
  9. Plane(A, A1, fOfA) → verticalPlane
  10. UnitVector(Vector[fOfA, Pu]) → fu
  11. IntersectPath(verticalPlane, f) → eq1
  12. Line(fOfA, secP) → g
  13. Point(A, Vector[(h * u)]) → Aplushu

AI Drawing Prompt Reference

Draw the gradient vector of a function f(x,y) and show its partial derivatives at point A. Construct a direction vector u and use it to define the directional derivative. Using point A1 and A, construct two unit vectors i and j to represent u. Then, draw the tangent plane perpendicular to f(x,y) at point A and a vertical plane through point A. Finally, illustrate the geometric meaning of the directional derivative, which is the projection of the intersection line between the vertical plane and the function surface onto the vertical plane.
The prompt above was compiled from the original drawing commands and is for reference only.