MIT 18.100B Real Analysis, Spring 2025 - Lecture 15: Derivatives; Laws for Differentiation

MIT 18.100B Real Analysis, Spring 2025 Instructor: Tobias Holck Colding View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG 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. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu Support OCW at http://ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.