When was the Chain rule first used?

[goodoldrebel]

Since Calculus has supposedly been around for a long time, when is there actual evidence of the chain rule first being used?

 

[Vagn]

Leibniz used it but didn't express it explicitly.
The first instance of it in it's modern form was in Lagrange's 1797 Théorie des fonctions analytiques.
http://en.wikipedia.org/wiki/Chain_rule#History

 

[goodoldrebel]

Leibniz used it but didn't express it explicitly.
The first instance of it in it's modern form was in Lagrange's 1797 Théorie des fonctions analytiques.
http://en.wikipedia.org/wiki/Chain_rule#History

Thanks for the input. I suspected that it's been a relatively recent form.

 

[HallsofIvy]

I can't imagine why you would think that. The chain rule is a necessity for differentiating all but the simplest functions.

 

[arildno]

I can't imagine why you would think that. The chain rule is a necessity for differentiating all but the simplest functions.

Well, but would take some time for matematicians to see the general pattern we call the chain rule, and then prove its generality.

For example, Euler's brilliant invention of modern day function notation (think it was him) simplified notationally what one was doing, enabling the discovery of the pattern.

 

[goodoldrebel]

I can't imagine why you would think that. The chain rule is a necessity for differentiating all but the simplest functions.

I understand that but its use has only been documented in the late 18th century (see above). Being used earlier in its complete format lacks verifiable evidence.