Derivatives of Inverse Hyperbolic Functions
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This example demonstrates the derivatives of inverse hyperbolic sine, cosine, tangent, etc., including their graphs and properties. Key math concepts involve inverse hyperbolic functions, derivative calculations, and graph transformations. GeoGebra commands like Curve, Cartesian, and Mirror are used for constructing the function curves and reflections. Suitable for high school and above students to learn the derivative properties of inverse hyperbolic functions in calculus.
GeoGebra Commands & Parameters
CurveCartesian(u_{1}, f_{2}'(u_{1}), u_{1}, 1, 10000) → f_{2}'CurveCartesian(u_{1}, f_{3}'(u_{1}), u_{1}, -1, 1) → f_{3}'CurveCartesian(u_{1}, f_{5}'(u_{1}), u_{1}, 0, 1) → f_{5}'CurveCartesian(u_{1}, f_{6}'(u_{1}), u_{1}, 1, 10000) → f_{6}'Mirror(f_{6}', yAxis) → b_1
AI Drawing Prompt Reference
In one coordinate system, plot several derivative graphs of inverse hyperbolic functions, showing curves for inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, and related cases. Construct each curve over its specified parameter range: one curve for u from 1 to 10000, another for u from −1 to 1, a third for u from 0 to 1, and again a curve for u from 1 to 10000. Then take one of these derivative curves and mirror it across the y-axis to display its y-axis symmetric counterpart, all shown together with the original curves for comparison.
The prompt above was compiled from the original drawing commands and is for reference only.