Visualizing derivatives

This video visually demonstrates the geometric meaning of derivatives using dynamic graphics. It begins by showing a curve and its tangent line at point x₀, then introduces a secant line connecting two points on the curve. As Δx decreases toward zero, the secant rotates closer to the tangent, illustrating the limiting process. The final formula defines the derivative as the limit of the secant slope — equivalent to the instantaneous rate of change or tangent steepness.

Before you watch

• Basic understanding of functions
• Slope concept from geometry
• Introductory exposure to limits