Differentiability and Continuity of Function, Rates of Change, Visual Proof, Example - Calculus

This video explains how differentiability implies continuity (3 conditions) of a function (e.g. composite or complex), including a basic introduction and visual proof using graphs and the limit formula, how to know if a function is differentiable at a point or when a function is not differentiable by first principles, and worked example practice questions. This topic is typically covered in class 11 or 12 maths. Understanding this topic is crucial to the chain, product and quotient rules, evaluating the derivatives of functions like sin, e^x, log and applying other differentiation rules.

📌 Worksheets are provided in PDF format to further improve your understanding:

- Questions Worksheet: https://drive.google.com/file/d/1-IfxXvhpMp43qxNG-21ZtIPqO4WMuvOk/view?usp=drive_link
- Answers: https://drive.google.com/file/d/1nchFi76DuCzBIx0TWesDVjlUz0qvNG7o/view?usp=drive_link

📌 Chapters on What You’ll Learn:

00:00 Differentiability and continuity
02:03 Worked example

📌 Perfect for calculus students and exam preparation, this tutorial uses plenty of examples and easy-to-follow explanations.

👉 Make sure to check out our full Calculus 1 and 2 course playlist, which covers differentiation, integration, sequences and series and their applications!

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