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Product Rule Demonstration

Product Rule Demonstration
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2016-01-10 13:43
FunctionCalculusDerivative
This example demonstrates the product rule in calculus. By constructing the graphs of two functions f(x) and g(x), and their product function h(x), it shows how to use the product rule to find the derivative of h(x). The construction summary mentions the use of commands like CurveCartesian, OrthogonalLine, Intersect, etc., in GeoGebra. Suitable for high school calculus students and educators.

GeoGebra Commands & Parameters

  1. CurveCartesian(u(t), v(t), t, 0, 10) → a
  2. OrthogonalLine(A, xAxis) → b
  3. OrthogonalLine(A, yAxis) → c
  4. OrthogonalLine(B, xAxis) → d
  5. OrthogonalLine(B, yAxis) → e
  6. Intersect(b, e) → C
  7. Intersect(c, d) → D
  8. Intersect(d, xAxis) → E
  9. Intersect(b, xAxis) → F
  10. Intersect(e, yAxis) → G
  11. Intersect(c, yAxis) → H
  12. Intersect(yAxis, xAxis) → I
  13. Polygon(G, H, A, C) → poly1, f, g, i, j
  14. Polygon(F, A, D, E) → poly2, k, l, m, n
  15. Polygon(H, A, F, E, B, G) → poly3, h_1, a_1, f_1, e_1, b_1, g_1
  16. Segment(G, H) → p
  17. Segment(F, E) → q