I heard someone say recently that Newton didn't know the chain rule. Is that true?

I know Newton didn't share our current conception of functions, the real line, limits, etc., so if he did use something like the chain-rule it wouldn't have been in its modern form. So what's the most chain-rule-like idea he did use (if he used anything close), and what did it look like in his notation?

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    $\begingroup$ See here. $\endgroup$ Commented Mar 12, 2022 at 21:08
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    $\begingroup$ Does this answer your question? When/How were the product and chain rules first proved? $\endgroup$
    – Spencer
    Commented Mar 13, 2022 at 13:17
  • $\begingroup$ I did read that question & answer before asking mine — it helps but seems incomplete, and I'm a bit confused by it. (It says that Leibniz only used the chain rule "implicitly", but like the commenter, I was under the impression that he explicitly used $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{\mathrm{d}y}{\mathrm{d}u}\frac{\mathrm{d}u}{\mathrm{d}x}$?) My question is — did Newton ever use the chain rule implicitly? (Or anything chain-rule-like that wasn't the "modern version"?) That link doesn't say. $\endgroup$ Commented Mar 13, 2022 at 15:16

1 Answer 1


I think Newton certainly used an equivalent of the chain rule, in that his "method" was to rip through a polyomial, multiplying each term by np/x (n = degree, p = x' or q = y', etc, x = x or y or whatever variable was targeted), which inserted chain rule-type "placeholders" everywhere they were needed. His interest was "the doctrine of curves", so he jumped right into solving multi-degree polynomial equations for tangents and integrals and his techniques were to that end.


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