Quotient Rule for Differentials

Theorem

Formulation 1

$\map \d {\dfrac y x} = \dfrac {x \rd y - y \rd x} {x^2}$

Formulation 2

$\map \d {\dfrac x y} = \dfrac {y \rd x - x \rd y} {y^2}$

Historical Note

The Quotient Rule for Differentials 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

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.19$: Leibniz ($\text {1646}$ – $\text {1716}$)