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The Chain Rule - How to REALLY Understand It

Using four different ways of looking at functions and their derivatives leads to a really solid understanding of the chain rule: what it means and why it's true.

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Visualizing the chain rule and product rule | Chapter 4, Essence of calculus
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Visualizing the chain rule and product rule | Chapter 4, Essence of calculus

The Derivative - The MOST Important Concept in Calculus
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The Derivative - The MOST Important Concept in Calculus

What Lies Between a Function and Its Derivative? | Fractional Calculus
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What Lies Between a Function and Its Derivative? | Fractional Calculus

The Subtle Reason Taylor Series Work | Smooth vs. Analytic Functions
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The Subtle Reason Taylor Series Work | Smooth vs. Analytic Functions

Lecture #9: How to Read so that you *Retain* Information
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Lecture #9: How to Read so that you *Retain* Information

The Most Misunderstood Concept in Math
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The Most Misunderstood Concept in Math

Limits, L'Hôpital's rule, and epsilon delta definitions | Chapter 7, Essence of calculus
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Limits, L'Hôpital's rule, and epsilon delta definitions | Chapter 7, Essence of calculus

HOLY ROSARY TODAY THURSDAY, JUNE 11, 2026 ST. JUDE THADDEUS & LUMINOUS MYSTERIES | DAILY HOLY ROSARY
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HOLY ROSARY TODAY THURSDAY, JUNE 11, 2026 ST. JUDE THADDEUS & LUMINOUS MYSTERIES | DAILY HOLY ROSARY

What is Jacobian? | The right way of thinking derivatives and integrals
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What is Jacobian? | The right way of thinking derivatives and integrals

Visual Demonstration of the Chain Rule
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Visual Demonstration of the Chain Rule

When CAN'T Math Be Generalized? | The Limits of Analytic Continuation
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When CAN'T Math Be Generalized? | The Limits of Analytic Continuation

The Obviously True Theorem No One Can Prove
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The Obviously True Theorem No One Can Prove

Train Your Brain to Never Forget (5 Feynman Habits)
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Train Your Brain to Never Forget (5 Feynman Habits)

Chain Rule Part 3: Why the Chain Rule Works
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Chain Rule Part 3: Why the Chain Rule Works

The hidden logic behind #, @, & and §
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The hidden logic behind #, @, & and §

My new favorite function?
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My new favorite function?

Integration by substitution (visualised)
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Integration by substitution (visualised)

Why Peter Scholze is once in a Generation Mathematician
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Why Peter Scholze is once in a Generation Mathematician

Olympiad level counting  (Generating functions)
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Olympiad level counting (Generating functions)

The Integral That Changed Math Forever
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The Integral That Changed Math Forever

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