Defining the Derivative (OpenStax Calculus Tutorial)

In this video, we dive into Chapter 3: Defining the Derivative from OpenStax Calculus. We work through six carefully chosen problems that highlight the difference between secant lines and tangent lines, and how the derivative is defined using limits. You’ll see step-by-step solutions that make the concept of the derivative clear and approachable. Whether you’re just starting calculus or brushing up on the basics, this walkthrough will help you build a strong foundation in differentiation. ⏱️ Timestamps 0:00 – Introduction 0:13 – Secant Line Slope: Linear Function 1:18 – Secant Line Slope: Square Root Function 2:07 – Tangent Line: Linear Derivative using definition 4:05 – Tangent Line: Quadratic Derivative using definition 6:57 – Derivative Using the Limit Definition: Linear Case 8:14 – Derivative Using the Limit Definition: Reciprocal Function 10:12 – Outro