Calculus Visualised: Why the Chain Rule Actually Works 🧐 скачать в хорошем качестве

Calculus Visualised: Why the Chain Rule Actually Works 🧐

Stop memorising calculus formulas and start understanding the "why" behind them. ⚙️🧠 -- Here is the interactive web lesson for this video so you can go through at your own pace or show your class: 🧐 https://alevelmaths.uk/lessons/chain-... Additionally, the perfect way to continue the exploration of this topic is by going onto Brilliant.org as this video is for the intuition and Brilliant.org actually takes you through the mathematical derivation which is the perfect next step after this video. 🚀 Also this link gets you 20% off: https://brilliant.org/alevelmaths/ -- The Chain Rule is one of the most vital concepts in Calculus, yet it is often taught as a rigid rule: dy/dx = dy/du * du/dx. But where does that multiplication come from? Why do we multiply the derivatives instead of adding them? In this video, we ditch the dry textbook definitions and build a deep, intuitive mental model using a system of gears. By visualizing functions as connected cogs spinning at different rates, we can see exactly how a change in "x" propagates through nested functions to affect "y". Whether you are a math student struggling with derivatives or a lifelong learner revisiting calculus, this visualisation will make the Chain Rule second nature. In this video, you will learn: The intuition behind nested functions like y = f(g(x)). How to visualise derivatives as the "spin rates" of gears. Why we multiply rates of change to find the final derivative. A step-by-step breakdown of the function y = (3x + 1)^5. TIMESTAMPS: 00:00 Introduction: Where does the rule come from? 00:13 The standard formula refresher 00:46 Historical Context (Leibniz & Newton) 00:54 The Intuition: The 3-Gear Analogy 01:24 The Example Problem: y = (3x + 1)^5 01:56 Visualizing the "X" Gear (Input) 02:13 Introducing the "Middle" Gear (u) 02:37 Calculating the First Link (du/dx) 03:07 Calculating the Second Link (dy/du) 04:10 Putting it Together: Multiplying the Rates 05:05 Moving from Intuition to Proof