Derivative of Trigonometric Functions

This GeoGebra example dynamically illustrates the derivatives of trigonometric functions (such as sine and cosine) by plotting both the original functions and their derivative curves. The core mathematical concepts involve the definition of the derivative and the differentiation rules for trigonometric functions, including that the derivative of sine is cosine and the derivative of cosine is negative sine. The construction uses the Derivative command on function objects f, g, and h to generate their respective derivative graphs, allowing side-by-side comparison in the graphing view. This is suitable for high school or introductory college calculus students to visualize the geometric meaning of derivatives as tangent slopes and to observe the periodic nature of trigonometric derivatives. By adjusting parameters or observing the curves, learners can deepen their intuitive understanding of differentiation and function transformations.