--- title: Derivatives description: Derivatives measure the instantaneous rate of change of a function. You will understand how to calculate derivatives using various rules, interpret them graphically as tangent lines, and use them to solve optimization problems and analyze the behavior of functions. category: mathematics subcategory: calculus difficulty: beginner, intermediate, advanced url: /subject/derivatives --- # Derivatives Derivatives measure the instantaneous rate of change of a function. You will understand how to calculate derivatives using various rules, interpret them graphically as tangent lines, and use them to solve optimization problems and analyze the behavior of functions. ## Available Resources 1 Videos • 2 Books • 3 Courses • 4 Websites ## Courses ### 1. Single Variable Calculus (MIT 18.01SC) **Author:** David Jerison 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. **Difficulty:** Beginner | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/ **Tags:** single-variable-calculus, derivatives, integrals, infinite-series ### 2. Introduction to Financial Engineering and Risk Management **Author:** Martin Haugh, Garud Iyengar 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. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/financial-engineering-intro **Tags:** financial-engineering, derivatives-pricing, binomial-model, black-scholes, fixed-income, term-structure ### 3. 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. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/differentiation-calculus **Tags:** courses, mathematics-statistics, calculus ## Websites ### 1. 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. **Difficulty:** Beginner | **Price:** Free **Link:** https://tutorial.math.lamar.edu/classes/calci/DerivativeIntro.aspx **Tags:** derivatives, calculus-1, differentiation, lecture-notes, worked-examples ### 2. Khan Academy Derivatives 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. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/differential-calculus **Tags:** derivatives, differential-calculus, limits, differentiation-rules, practice-exercises ### 3. 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. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.khanacademy.org/math/calculus-1 **Tags:** calculus, derivatives, integrals, optimization ### 4. mathsisfun.com MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathsisfun.com **Tags:** websites, mathematics-statistics, algebra ## Videos ### 1. 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. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/watch?v=9vKqVkMQHKk **Tags:** derivatives, calculus-intuition, rate-of-change, limits, 3blue1brown ## Books ### 1. Calculus: An Intuitive and Physical Approach **Author:** Morris Kline Dover reprint of Kline's second-edition calculus textbook, which motivates each idea through physical and scientific problems. Readers work through derivatives, integration techniques, and applications while building intuition for why calculus methods work, not just how. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0486404536?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, calculus ### 2. Calculus with Analytic Geometry **Author:** George F. Simmons Single- and multivariable calculus textbook by George F. Simmons, known for clear exposition, historical notes, and biographical appendices. Readers develop a working command of differentiation, integration, series, and analytic geometry with applications to physical problems. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0070574197?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, calculus --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. 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