Differentiation of Exponents: Tangent Slopes

This GeoGebra example dynamically illustrates the derivative of an exponential function by showing the tangent line at a movable point. The core mathematical concept is the differentiation rule for exponential functions and the geometric interpretation of the derivative as the slope of the tangent. The construction uses the Tangent command to draw the tangent to the function f at point A, and the Root command to find relevant intersections or zeros. Additional objects such as points B and C, segments d and e, and text labels (text1 to text4) are used to display the slope value and function expression. This is suitable for high school or introductory college calculus students to visualize how the derivative of an exponential function changes, and serves as an effective classroom demonstration to connect the abstract derivative formula with the intuitive tangent line graph.