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Derivative of a Product of Functions

Derivative of a Product of Functions
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2016-10-05 01:29
FunctionCalculusDerivative
This example demonstrates the derivative of a product of two functions. Key mathematical concepts include derivatives and the product rule. Functions f and g are constructed, and tangent lines are drawn using the Tangent command. Slope is calculated with the Slope command, and key points are created using the Point command. Suitable for high school math education and learning derivative concepts.

GeoGebra Commands & Parameters

  1. Tangent(C, h) → i
  2. Tangent(A, f) → j
  3. Tangent(B, g) → k
  4. Circle(A, 1) → c
  5. Circle(B, 1) → d
  6. Circle(C, 1) → e
  7. Slope(j) → m
  8. Slope(k) → m_1
  9. Slope(i) → m_2
  10. Point(g) → D
  11. Point(g) → E
  12. Distance(D, E) → distanceDE
  13. Point(f) → F
  14. Point(f) → G
  15. Distance(G, F) → distanceGF
  16. Distance(H, I) → distanceHI

AI Drawing Prompt Reference

Draw two function curves representing two differentiable functions. Place two points on each curve and connect each pair to show the change. On each curve, select one point and draw its tangent line, displaying the slope. Construct a third function as the product of the first two, and on its curve select a point, draw the tangent line, and show its slope. Mark the three key points with small circles. Finally, measure and display the distances between the two points on each of the two original curves, and also the distance between two points on the product curve.
The prompt above was compiled from the original drawing commands and is for reference only.