Derivative of Cosine at x=0: cos'(0)=0

① This interactive GeoGebra example visually demonstrates that the derivative of the cosine function at x=0 is zero, i.e., cos'(0)=0. ② It covers core calculus concepts: the definition of the derivative as a limit, the slope of the tangent line, and local linear approximation. ③ The construction uses GeoGebra commands such as Point, Function, Derivative, Intersect, Segment, Line, Polygon, and Sequence to plot f(x)=cos(x), compute the derivative at x₀=0, and draw the tangent line. Sliders, input boxes, and buttons allow users to vary parameters and observe how the secant slope approaches the tangent slope as Δx→0. ④ Suitable for high school and early college students learning introductory calculus, this example serves as a visual aid for classroom instruction or self-study of derivative concepts.