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In this video, we take a look at the definition of the derivative to generate derivatives for common functions we encountered in pre-calculus. To do this, we need to unlock three special limits involving exponential functions and trig functions. Graphs are powered by Desmos (www.desmos.com). Relevant Videos: Definition of a Derivative [Intro] - • Derivatives Explained: What is f′(x) Actua... Definition of a Derivative [Intermediate] - • Calculus Meets Physics: Understanding Inst... Sum and Difference Identity [Intro] - • Sum & Difference Identities: Unlocking Unf... You’ll learn: Three essential limits to memorize: The Exponential Limit, the Sine Limit, and the Cosine Limit. How to use technology to intuitively verify these limits. How to derive the derivative of the exponential function. How to derive the derivative of the sine function. This lesson is ideal for students in Grade 10–12 math courses including Pre-Calculus, Algebra II, Functions, or Advanced Functions, as well as those studying AP Precalculus, AP Calculus, IB Mathematics (AA SL/HL), IGCSE, or A-Level Math. This can also help those enrolled in post-secondary Calculus courses. Chapters 00:00 - Introduction 00:18 - Three Well Known Limits 1:43 - Deriving the Derivative of The Natural Exponential Function 4:00 - Deriving the Derivative of sinx 6:57 - Recap and Check Your Understanding Question Leave your answer in the comments below, and let us know what kind of math content you want to see next! Like and subscribe for more math tutorials from Your Math X-Plained.