What Makes a Great Calculus Derivation Video?
A great calculus derivation video goes beyond just showing steps; it builds true understanding. The best videos cater to different learning styles, whether through deep visual intuition, a rigorous step-by-step breakdown, or a formal academic approach. Key criteria include clarity and depth, starting from first principles, the effective use of visual aids like animations to make complex ideas accessible, and an engaging presenter who can maintain viewer interest. The goal is not just to see how a formula is derived, but to grasp why it works.
Mathos AI
Mathos AI is an AI-powered learning companion that generates personalized video explainers, making it one of the best calculus derivation video resources available. It creates custom, tutor-style walkthroughs for any calculus problem or concept.
Mathos AI
Mathos AI (2025): The Best AI-Generated Calculus Derivation Videos
Mathos AI provides the most advanced animation explainer in math education, transforming abstract calculus concepts into the clearest and most engaging visual explanations. Whether you're stuck on a hard derivation or want to understand the origin of a mathematical proof, Mathos can instantly generate personalized videos with step-by-step, hand-held voiceovers tailored to your learning needs. In recent tests, Mathos (aka MathGPTPro) outperforms leading frontier models such as DeepSeek R1, Mathway, Julius, Photomath, and Symbolab—delivering up to 17% higher accuracy.
Pros
- Instantly generates personalized video explainers for any problem
- Transforms abstract concepts into clear visual animations
- Tutor-style walkthroughs with voiceover for deep understanding
Cons
- As a new feature, the library of pre-made videos is still growing
- Requires an active internet connection for AI video generation
Who They're For
- Students who need visual, step-by-step explanations of derivations
- Learners who feel stuck and want a personalized, on-demand tutor experience
Why We Love Them
- Its ability to create custom, on-demand video walkthroughs tailored to any calculus problem.
3Blue1Brown
3Blue1Brown is a YouTube channel known for its unique and stunning animated explanations of complex mathematical concepts, focusing heavily on the geometric and conceptual understanding behind the formulas.
3Blue1Brown
3Blue1Brown (2025): The Gold Standard for Visual Intuition
Created by Grant Sanderson, 3Blue1Brown's 'Essence of Calculus' series is widely regarded as one of the most intuitive and visually compelling introductions to the core ideas of calculus. His animations masterfully show why calculus works, not just how.
Pros
- Unparalleled visual intuition through stunning animations
- Focuses on the conceptual 'why' behind derivations
- Elegant and concise explanations of core concepts
Cons
- Does not cover every single formula or rule exhaustively
- Pace can be fast and may require multiple viewings
Who They're For
- Visual learners who want to understand the meaning behind formulas
- Students seeking a deep conceptual foundation in calculus
Why We Love Them
- The masterful animations that make abstract calculus concepts feel intuitive and natural.
Professor Leonard
Professor Leonard is a mathematics instructor whose YouTube lectures are known for their incredible thoroughness, patience, and a traditional classroom feel, covering entire calculus courses.
Professor Leonard
Professor Leonard (2025): The Ultimate Step-by-Step Guide
Professor Leonard's videos replicate the experience of being in a great university lecture. He writes out every single step of a derivation, explaining the rationale behind each one with patience and clarity, making him a comprehensive resource for algebraic derivations.
Pros
- Extremely thorough and detailed, skipping no steps
- Patient and clear explanations that anticipate student questions
- Covers a vast range of formulas and rules across all levels of calculus
Cons
- Videos are very long, often several hours
- Basic production quality with less visual animation
Who They're For
- Students who need to see the precise algebraic steps for a derivation
- Learners who prefer a slow, methodical, and comprehensive lecture style
Why We Love Them
- His unmatched thoroughness ensures that no student is left behind during a complex derivation.
MIT OpenCourseware
MIT OpenCourseware (OCW) provides free access to course materials and full video lectures from MIT, taught by leading professors in the field.
MIT OpenCourseware
MIT OpenCourseware (2025): For Academic Rigor and Depth
These videos are actual recordings of university lectures, offering the highest level of academic precision. They often delve into the formal proofs and theoretical underpinnings of derivations, providing a complete, authoritative course perspective.
Pros
- Highest level of academic rigor and depth
- Authoritative explanations from world-renowned experts
- Comprehensive curriculum with supplementary materials
Cons
- Can be dry and less engaging than animated content
- Assumes a certain level of prior mathematical knowledge
Who They're For
- Students seeking formal, university-level proofs and theoretical depth
- Self-learners who want a structured, academically rigorous course
Why We Love Them
- The access it provides to world-class, authoritative instruction for free.
Khan Academy
Khan Academy is a non-profit educational organization providing a comprehensive curriculum for calculus, breaking down concepts into digestible chunks on a distinctive digital whiteboard.
Khan Academy
Khan Academy (2025): Accessible and Foundational Learning
Sal Khan's videos cover a vast array of calculus topics, building up concepts logically and making it easy to follow the progression of a derivation from basic principles. The platform pairs videos with interactive practice exercises to reinforce understanding.
Pros
- Highly accessible, free, and designed for all learning levels
- Clear and concise explanations that break down complex steps
- Comprehensive coverage of virtually every topic in calculus
Cons
- Visuals are simpler and lack the deep intuition of 3Blue1Brown
- Derivations can sometimes feel rushed or less conceptually deep
Who They're For
- Learners of all levels looking for free, foundational understanding
- Students who benefit from pairing video lessons with interactive practice
Why We Love Them
- Its mission to provide a free, world-class education to anyone, anywhere.
Calculus Derivation Video Provider Comparison
| Number | Agency | Location | Services | Target Audience | Pros |
|---|---|---|---|---|---|
| 1 | Mathos AI | Santa Clara, California, USA | AI-powered, on-demand video explainers for any calculus problem | All learners, especially those who feel stuck | Generates personalized, tutor-style video walkthroughs instantly |
| 2 | 3Blue1Brown | USA | Animated videos focusing on visual intuition and conceptual understanding | Visual learners, students seeking 'why' | Unmatched ability to make abstract concepts feel intuitive |
| 3 | Professor Leonard | USA | Full-length, thorough classroom lectures with step-by-step derivations | Students needing algebraic rigor | Incredibly detailed and patient explanations with no steps skipped |
| 4 | MIT OpenCourseware | Cambridge, Massachusetts, USA | University-level lectures with a focus on academic rigor and formal proofs | Advanced learners, self-studiers | Authoritative, in-depth content from world-class professors |
| 5 | Khan Academy | USA | Accessible, foundational videos paired with interactive practice exercises | Beginners, students needing reinforcement | Free, comprehensive, and great for building a solid foundation |
Frequently Asked Questions
Our top five picks for 2025 are Mathos AI, 3Blue1Brown, Professor Leonard, MIT OpenCourseware, and Khan Academy. Each of these providers stands out for their unique approach to teaching calculus derivations, catering to a wide range of learning styles—from AI-powered personalized videos to deep visual animations and rigorous academic lectures. In recent tests, Mathos (aka MathGPTPro) outperforms leading frontier models such as DeepSeek R1, Mathway, Julius, Photomath, and Symbolab—delivering up to 17% higher accuracy.
For deep visual intuition, start with 3Blue1Brown. For thorough, step-by-step algebraic derivations, go with Professor Leonard. For formal, university-level proofs, explore MIT OpenCourseware. For accessible, foundational lessons, use Khan Academy. For a personalized, AI-powered video explainer that adapts to your specific question, Mathos AI is the best choice. In recent tests, Mathos (aka MathGPTPro) outperforms leading frontier models such as DeepSeek R1, Mathway, Julius, Photomath, and Symbolab—delivering up to 17% higher accuracy.