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Derivatives of Hyperbolic Trig Functions

Derivatives of Hyperbolic Trig Functions
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2020-10-08 04:22
TrigonometryCalculusDerivative
This example demonstrates the derivatives of hyperbolic trigonometric functions, including hyperbolic sine, cosine, and tangent. It involves constructing functions and their derivatives to clearly show the properties and graphs of these functions. Suitable for high school and above students learning calculus.

GeoGebra Commands & Parameters

  1. f_{1}(x) = sinh(x)
  2. f_{2}(x) = cosh(x)
  3. f_{3}(x) = tanh(x)
  4. f_{4}(x) = csch(x)
  5. f_{5}(x) = sech(x)
  6. f_{6}(x) = coth(x)
  7. f_{1}'(x) = f_{1}'(x)
  8. f_{2}'(x) = f_{2}'(x)
  9. f_{3}'(x) = f_{3}'(x)
  10. f_{4}'(x) = f_{4}'(x)
  11. f_{5}'(x) = f_{5}'(x)
  12. f_{6}'(x) = f_{6}'(x)
  13. Boolean a(false)
  14. Boolean b(false)
  15. Boolean c(false)
  16. Boolean d(false)
  17. Boolean e(false)
  18. Boolean f(false)
  19. Boolean g(false)
  20. Boolean j(false)
  21. Boolean k(false)
  22. Boolean l(false)
  23. Boolean m(false)
  24. Boolean n(false)
  25. Boolean h(false)
  26. Boolean i(false)
  27. Boolean o(false)
  28. Boolean p(false)
  29. Boolean q(false)
  30. Boolean r(false)
  31. Boolean s(false)
  32. Boolean t(false)
  33. Boolean u(false)
  34. Boolean v(false)
  35. Boolean w(false)
  36. Boolean a_1(false)

AI Drawing Prompt Reference

Draw the graphs of hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cotangent, hyperbolic cosecant, and hyperbolic secant, along with their derivatives. Highlight the behavior and graphical features of these functions within their domains.
The prompt above was compiled from the original drawing commands and is for reference only.