Differential of Logarithm of Quotient

Theorem

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

Proof

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Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 2.9$: Integrating Factors: $(16)$