0
$\begingroup$

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?

Improve this question
$\endgroup$
3
  • 2
    $\begingroup$ See here. $\endgroup$
    – Moishe Kohan
    Mar 12, 2022 at 21:08
  • 3
    $\begingroup$ Does this answer your question? When/How were the product and chain rules first proved? $\endgroup$
    – Spencer
    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. $\endgroup$
    – greatBigDot
    Mar 13, 2022 at 15:16

1 Answer 1

Reset to default
1
$\begingroup$

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.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.