Effect of Stretches on the Derivative

①This example dynamically demonstrates how the derivative of a function changes when the function is stretched horizontally or vertically. ②Core mathematical concepts include derivatives, function transformations (stretches), the chain rule, and the geometric interpretation of tangent slopes. ③Construction highlights: Using GeoGebra, functions f and its derivative f' are created, along with stretched versions g, h and their derivatives g', h', with sliders or commands controlling the stretch factors to observe the resulting derivative graphs. ④Suitable for high school to early college calculus students, this helps visualize the effect of stretches on derivatives and reinforces the geometric meaning of the chain rule.