Product Rule for Differentials

Theorem

$\map \d {x y} = x \rd y + y \rd x$


Proof


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Historical Note

The was stated, without proof or explanation, by Gottfried Wilhelm von Leibniz in his $1684$ article Nova Methodus pro Maximis et Minimis, published in Acta Eruditorum.


Sources

  • 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 2.9$: Integrating Factors: $(13)$
  • 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.19$: Leibniz ($\text {1646}$ – $\text {1716}$)
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