Khan Academy Derivatives
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Khan Academy's free differential calculus course, combining short video lessons with graded practice on limits, continuity, the derivative definition, differentiation rules, and applications such as optimization. Learners build fluency computing derivatives and applying them to problems.
More resources on Derivatives
Introduction to Financial Engineering and Risk Management
Columbia University's introductory course in financial engineering, reviewing probability and optimization, then pricing fixed income securities and swaps, and valuing options with one-period and multi-period binomial models and Black-Scholes. Learners can price standard derivatives in an arbitrage-free framework.
Single Variable Calculus (MIT 18.01SC)
MIT's self-paced 18.01SC covers differentiation, applications of derivatives, integration, techniques of integration, and infinite series, with problem sets, recitation videos, and exams with solutions. Completing it gives the standard first-semester calculus foundation.
Paul's Online Math Notes
Paul Dawkins' free Calculus I notes from Lamar University, covering the definition of the derivative, differentiation rules, implicit differentiation, and related rates, with worked examples and practice problems. Learners can compute and interpret derivatives confidently.
The Paradox of the Derivative
Chapter 2 of 3Blue1Brown's Essence of Calculus series, a 15-minute animated explanation of why "instantaneous rate of change" sounds paradoxical and how the derivative resolves it as the limit of rates over shrinking intervals.
Khan Academy - Calculus Applications
Khan Academy's Calculus 1 course covers derivatives, integrals, and their applications to optimization, related rates, and area/volume problems, with practice exercises and video explanations for each topic.
Calculus 1: Differentiation
Part two of Robert Ghrist's five-part University of Pennsylvania single-variable calculus sequence, covering derivatives, differentiation rules, linearization, higher derivatives, optimization, and differential operators, using Taylor series throughout. Emphasizes conceptual understanding over rote computation.