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Derivative of Inverse Secant Function

Derivative of Inverse Secant Function
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2015-06-23 23:08
FunctionTrigonometryCoordinate GeometryCalculusDerivative
This example demonstrates the derivative of the inverse secant function. Key mathematical concepts include derivatives and trigonometric functions. Using GeoGebra commands such as Vector, Point, Function, Segment, CurveCartesian, etc., the inverse secant function and its derivative can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Vector(XOl, XOr) → u
  2. Vector(YOd, YOu) → v
  3. Vector(XDl, XDr) → w
  4. Vector(YDd, YDu) → z
  5. Point(u) → A
  6. Function(1 / ((abs(x) * (x^(2) - 1)^(1 / 2))), x(XOl), x(XOr)) → gO
  7. Function(gO(x) + td, x(XOl), -1.02) → gl
  8. Segment(AD, E) → e
  9. Function(1 / cos(x), 0, 3.141592653589793) → fO
  10. CurveCartesian(fO(t), t, t, 0, 3.141592653589793) → f
  11. Intersect(fO, b, (-10.134889463046562, -1.3187580843257427)) → B
  12. Tangent(B, fO) → d
  13. Mirror(d, h) → t
  14. OrthogonalLine(G, u) → i
  15. Intersect(t, i) → H
  16. Polygon(C, G, H) → poly1, h_1, c_1, g_1
  17. Function(gO(x) + td, 1.02, x(XOr)) → gr
  18. Segment(AD, O) → g
  19. Segment((-1, y(YDd)), (-1, y(YDu))) → q
  20. Segment((1, y(YDd)), (1, y(YDu))) → r
  21. OrthogonalLine(A, u) → c
  22. Intersect(c, f) → R, R_1
  23. Segment(A, R) → p
  24. Tangent(R, f) → s
  25. Slope(s) → m_t

AI Drawing Prompt Reference

Draw the graph of the inverse secant function and its derivative. First, plot the inverse secant function, then draw its tangent at a specific point, followed by the mirror image of the tangent and horizontal line segments. Finally, draw the tangent of the inverse secant function at another point and indicate its slope.
The prompt above was compiled from the original drawing commands and is for reference only.