Lecture 15: Derivatives; Laws for Differentiation

MIT 18.100B Real Analysis, Spring 2025
Instructor: Tobias Holck Colding
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We define what it means for a function to be differentiable. We show that if a function is differentiable at a point, then it is also continuous. We then establish the basic algebraic laws for differentiation. Those includes Leibniz's rule, the quotient rule, and the chain rule. Once we have that, we prove Rolle's lemma and use it to show the mean value theorem.

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Post from MIT OpenCourseWare on September 02, 2025

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