Inverse Trig Functions and Their Derivatives

This GeoGebra applet visualizes inverse trigonometric functions (such as arcsin, arccos, arctan) and their derivatives by dynamically computing the slope of tangent lines at selected points. The core mathematical concepts include the definition of inverse trig functions, the relationship between derivatives and tangent slopes, and the graphical correspondence between a function and its derivative. Construction highlights: the applet uses RandomElement and Element to generate random points, Mirror to create symmetric inverse function graphs, Tangent and Slope to draw tangent lines and compute their slopes, and multiple text objects (text1 to text6_1) to display real-time numerical values. Suitable for high school to college-level calculus instruction, this applet helps students understand derivative formulas for inverse trig functions and their geometric interpretation, and can also be used for independent exploration of how derivatives vary across different inverse trig functions.