The Chain Rule is a method for finding complex derivatives and is used all the time in Statistics and Machine Learning. This video breaks it down into its two simple pieces and shows you how they easily come together. We then use the Chain Rule to solve a common Machine Learning problem - optimizing the Residual Squared Loss Function. English This video has been dubbed using an artificial voice via https://aloud.area120.google.com/ to increase accessibility. You can change the audio track language in the Settings menu. Spanish Este video ha sido doblado al español con voz artificial con https://aloud.area120.google.com/ para aumentar la accesibilidad. Puede cambiar el idioma de la pista de audio en el menú Configuración. Portuguese Este vídeo foi dublado para o português usando uma voz artificial via https://aloud.area120.google.com/ para melhorar sua acessibilidade. Você pode alterar o idioma do áudio no menu Configurações. For a complete index of all the StatQuest videos, check out: https://statquest.org/video-index/ If you'd like to support StatQuest, please consider... Buying my book, The StatQuest Illustrated Guide to Machine Learning: PDF - https://statquest.gumroad.com/l/wvtmc Paperback - https://www.amazon.com/dp/B09ZCKR4H6 Kindle eBook - https://www.amazon.com/dp/B09ZG79HXC Patreon: https://www.patreon.com/statquest ...or... YouTube Membership: null ...a cool StatQuest t-shirt or sweatshirt: null ...buying one or two of my songs (or go large and get a whole album!) https://joshuastarmer.bandcamp.com/ ...or just donating to StatQuest! https://www.paypal.me/statquest Lastly, if you want to keep up with me as I research and create new StatQuests, follow me on twitter: https://twitter.com/joshuastarmer 0:00 Awesome song and introduction 2:02 A super simple example 6:32 A slightly more complicated example 9:16 The Chain Rule when the relationship is not obvious 11:47 The Chain Rule for the Residual Sum of Squares Corrections: 13:05 When the residual is negative, the pink circle should be on the left side of the y-axis. And when the residual is positive, the pink circle should be on the right side. #StatQuest #TheChainRule #DubbedWithAloud