Differentiation - The Chain Rule

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The Chain Rule is one of most important rules in differentiation and allows us to find the derivative of composite functions. This rule alone allows to differentiate an infinite number of different functions and combined with the product rule, allows us to solve almost every differentiation problem!

Timestamps:
00:00 - Intro
00:16 - The Composition of Functions
01:04 - The Chain Rule
01:21 - Examples
03:29 - The Extended Chain Rule
05:19 - Substitutions for the Chain Rule
07:11 - Number one tip for the Chain Rule
08:47 - Proof of the Chain Rule
  1. Mathacy
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Комментарии
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Here before this blows up! Amazing explanation.

karimjanmohamed
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Truly underrated channel! Hope you get more followers in future!

semyonbelov
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Your videos just keep getting better and better! 🔥 Love the Mario reference! Best explanation of the chain rule out there 👏

aleenavirdee
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Amazing explanation, one of the best I have seen!

Dineshlol
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Amazing tutorial ! Learnt a lot ! Genuinely the best maths YouTuber out there 🙏

DiLLZGFX
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Love seeing the graphs, so helpful when understanding

TheHashCam
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Fantastic explanation, very thorough and very helpful. :)

aaronnanoo
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Well done!
Very helpful and explained very well.

zoyasadiq
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For a long time I struggled to understand the structural reason why composition of functions turns into multiplication. That is, why is multiplication the natural thing to do? And why is the formula so asymmetric, while it‘s totally nice for addition for example, where it‘s just (f + g)' = f' + g'. My confusion was resolved when I learned that taking the tangent space at a point is a functor from pointed manifolds to vector spaces.

hdbrot
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4:03 too many brackets, y=f1(f2…fn(x)…), only 4, 2 sets of 2.

arlenestanton
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you told where chain rule is used; but u didn't let us see how chain-rule 'works' with graph!

voongvaang
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I didnt understand the proof nor how to substitute but i think the vid is very well made maybe i just need to review derivatives plus how to assign functions

abbasfadhil