# When was the Chain rule first used?

• goodoldrebel
In summary, the chain rule has been around for a long time, but the first documented instance of its modern form was in Lagrange's 1797 Théorie des fonctions analytiques. It is possible that it was used earlier but there is no verifiable evidence of this. The use of modern function notation by Euler also aided in the discovery of the pattern.
goodoldrebel
Since Calculus has supposedly been around for a long time, when is there actual evidence of the chain rule first being used?

Vagn said:
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.

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

HallsofIvy said:
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.

HallsofIvy said:
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.

## 1. What is the Chain Rule?

The Chain Rule is a mathematical rule used in calculus to find the derivative of a composite function. It states that the derivative of a composite function is equal to the product of the derivatives of its individual functions.

## 2. Who first discovered the Chain Rule?

The Chain Rule was first discovered by the German mathematician Gottfried Wilhelm Leibniz in the late 17th century. However, it was not published until years later in his work "Nova Methodus pro Maximis et Minimis".

## 3. When was the Chain Rule first used in a mathematical proof?

The Chain Rule was first used in a mathematical proof in the early 18th century by Leibniz. In his work "De Geometria" published in 1716, he used the Chain Rule to solve problems related to the calculation of tangents and extrema.

## 4. How has the Chain Rule evolved over time?

The Chain Rule has evolved over time to become an essential tool in calculus and other branches of mathematics. It has been generalized to include higher order derivatives and has been extended to multivariable calculus. It has also been applied in various fields, including physics, engineering, and economics.

## 5. Why is the Chain Rule important?

The Chain Rule is important because it allows us to find the derivative of complex functions by breaking them down into simpler functions. It is a fundamental concept in calculus and is used in many real-world applications. Without the Chain Rule, it would be challenging to solve problems involving rates of change and optimization.

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