Why is it Called the Chain Rule?

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Ever wondered why the Chain Rule is called the Chain Rule? I’ll give you a hint: it doesn’t have to do with the Chainsmokers, chain link fences, or chain restaurants. Watch this video to learn about chain drive systems and why I believe they are the origin of the Chain Rule’s name.

Licensed under Creative Commons: By Attribution 3.0

Marc Renault gave permission to use animations from his page on the Intuitive Notion of the Chain Rule:

Project Manager: Libby Farrell

[Theflydark]

I believe that "chain" only means "things following each other". Like a chain reaction. Same in french: "réaction en chaîne".

[WHErwin]

i used to have problems understanding the chain rule but this really helps me understand the reasoning behind it

[mikeymasi]

Simple and concise explanation, well done

[staffehn]

I don’t know where you searched for “𝗞𝗲𝘁𝘁𝗲𝗻regel” but the German Wikipedia makes the connection obvious by describing it as a rule that “makes statements about the derivation of a function, which can be represented as a composition of two differentiable functions” in the second sentence, where it uses the German word “Ver𝗸𝗲𝘁𝘁ung” (usual word meaning: chain / concatenation / linkage – the word most literally is translated as en𝗰𝗵𝗮𝗶𝗻ment) which is one of the possible German terms for mathematical composition.
I also found the word chain used in English for “method chaining”, which is basically the composition of method calls in computer science.
Indeed very interesting though, that the rule is called “chain” rule in English where there’s, as far as I can tell, no connection of the word to function composition.
At least all the other rules use names that *do* use the correct English terms for the respective operations, like “product”, “quotient”, “reciprocal”, “polynomial” or “power” rule.

[ P.S. — goddammit spam filter, won’t you like Unicode for 𝗯𝗼𝗹𝗱 text? I would use the *markup* if I could but it won’t work *mid*word :/ ]

[adolfocarrillo]

Excellent analogy to the Chain Rule, 🥑So here the Chain Rule is applied to the Rotational Speed or Angular Speed between the gears or pulleys, acknowledging 🥑the fact that Tangencial Speed in the sistem remains constat. Your are a genius, Thanks.🥑😋

[mariebcfhs]

Kette wurde getroffen! Wir sind bewegungsunfähig!

[Jop_pop]

The video has 301 views rn this is such a throwback

[koenth]

Product rule handles the derivative of a product
quotient rule does the derivative of a quotient,
chain rule does the derivative of a chain function f(g(x)), where the functions apply one after the other, as shackles in a chain if you like. What is 'too simplistic' about that?
For the rotation ratio you mention, we could do with just gears, so why get chains involved?? Very unlikely.

[Ibakecookiess]

I get lost at 2:25, can somebody expand on it a bit? I don't see how his conclusion follows from what he just said.

[BigDBrian]

"these are not fractions"
actually, they kind of are.