Derivative Visualizer

Visualize functions and their derivatives with interactive tangent line exploration

Overview

The Derivative Visualizer provides an interactive platform for exploring derivatives, tangent lines, and instantaneous rates of change. Visualize how derivatives describe the slope of a function at any point and explore the relationship between a function and its derivative.

Tips

1. Start with simple polynomials like x² or x³ to build intuition about how derivatives work
2. Observe where the derivative crosses zero - these correspond to critical points (maxima or minima) on the original function
3. Move the tangent line point to see how the slope changes continuously along the curve
4. Compare the function and derivative graphs side by side to notice patterns, such as how the derivative of a polynomial has one degree less than the original
5. Try trigonometric functions like sin(x) to see the cyclic relationship between sin, cos, and their derivatives