Chain rule
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- Date
- 1676 · confidence medium
- Place
- Paris, France
- Credited to
- Gottfried Wilhelm Leibniz
- Field
- Knowledge & symbols
What was discovered
Leibniz first applied, in a 1676 manuscript, the rule for differentiating a composite function, while computing the derivative of √(a + bz + cz²). The modern formulation would come over a century later with Lagrange (1797) and Cauchy (1823).
The 1676 manuscript contained a sign error; the rule does not appear in Euler's analysis texts despite being later.
What it led to
- Modern formulation by Lagrange (1797) and Cauchy (1823)
- Backpropagation algorithm in neural networks
Built on
- Leibnizian calculus and notation1675
- Leibniz's differential calculus