The paradox of the derivative | Chapter 2, Essence of calculus

What is an "instantaneous rate of change" when change happens across time? Help fund future projects: https://www.patreon.com/3blue1brown This video was supported in part by Art of Problem Solving: https://aops.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/lessons/derivatives#thanks Home page: https://www.3blue1brown.com/ Note, to illustrate my point for the target audience of a new calculus student, I discussed a hypothetical speedometer that makes distance measurements over a very small time. Interestingly, most actual speedometers in modern cars work by analyzing the induced current of a spinning magnet, which is in some sense the universe implementing the derivative. Thanks to these viewers for their contributions to translations Dutch: @LFWarsen Hebrew: Omer Tuchfeld Italian: mulstato Vietnamese: @ngvutuan2811 ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown