The Derivative as a Function (Applying the Difference Quotient)

📘 In this OpenStax Calculus Ch. 3 §2 walkthrough, we start by computing a derivative directly from the limit (difference quotient) for a linear function and explain why a constant slope yields a constant derivative. The focus is on precise algebra, correct limit handling, and why each simplification step is valid. If this helped, please like and subscribe! Timestamps: 00:00 – Introduction 00:14 – Problem 55 - Derivative from definition; difference quotient; simplify. 02:02 – Problem 57 - Difference quotient derivative; expand and cancel terms. 03:47 – Problem 59 - Derivative from definition; rationalize radical numerator. 07:34 – Problem 65 - Sketch f' from graph; use slopes insight. 09:41 – Problem 69 - Identify derivative from limit; find f'(a). 11:32 – Problem 71 - Recognize difference quotient; compute derivative at point. 12:35 – Outro #Calculus #Math #ScalarLearning #APCalculus #Derivatives #DifferenceQuotient #ConjugateMethod #GraphingDerivatives #Limits #OpenStax