MathPlotAI Logo MathPlotAI

Derivative of Inverse Function Rule

Derivative of Inverse Function Rule
Loading the math board and drawing, please wait…
2020-10-06 03:26
FunctionCalculusDerivative
This example demonstrates the derivative of the inverse function rule. Key mathematical concepts include derivatives and inverse functions. Using GeoGebra commands such as Mirror, Intersect, and Segment, the inverse function's graph is constructed, and the properties of its derivative are observed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Textfield(f) → InputBox1
  2. Mirror(f, id) → f_{1}
  3. Textfield(a) → InputBox2
  4. OrthogonalLine(A, xAxis) → h
  5. Intersect(h, f_{1}) → B
  6. Segment(B, D) → k
  7. Vector(D, E) → u
  8. Midpoint(D, E) → F
  9. Vector(G, H) → v
  10. Midpoint(G, H) → I
  11. Mirror(B, id) → B'
  12. Segment(B', G) → m
  13. Segment(B', B) → p
  14. Midpoint(B', B) → C
  15. Textfield(g) → InputBox3

AI Drawing Prompt Reference

Draw a graph of an inverse function, showing its mirror relationship with the original function. Construct a vertical line intersecting the inverse function graph, then use mirroring to obtain symmetric points, and connect these points to form the inverse curve. Ensure the graph is clear and label key points to help understand the properties of the inverse function.
The prompt above was compiled from the original drawing commands and is for reference only.