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Derivatives from First Principles

Derivatives from First Principles
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2016-05-08 15:37
Coordinate GeometryCalculusDerivative
This example demonstrates how to derive the derivative of a function from first principles, involving core math concepts like the definition of a derivative, limits, slope, and distance. It uses GeoGebra commands and objects such as Point, Segment, OrthogonalLine, Intersect, LaTeX, Polygon, Slope, Distance, Text, and Midpoint. Suitable for high school and above students to understand the essence of derivatives.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Point(f) → B
  3. Segment(A, B) → g
  4. OrthogonalLine(B, xAxis) → h_3
  5. OrthogonalLine(A, h_3) → i
  6. Intersect(h_3, i) → D
  7. Segment(A, D) → h
  8. Segment(B, D) → l
  9. LaTeX(l, true, true) → text1
  10. LaTeX(h, true, true) → text2
  11. Polygon(B, A, D) → poly1, d, b, a
  12. Slope(g) → m
  13. Distance(A, B) → AB
  14. Text(slope) → text8
  15. Midpoint(l) → E
  16. Midpoint(h) → F