Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 13/Rules for Differentials

Rule for Differentials
The rules for differentials are exactly analogous to those for derivatives.
 * $13.52$: $\mathrm d \left({u \pm v \pm w \cdots}\right) = \mathrm d u \pm \mathrm d v \pm \mathrm d w \pm \cdots$


 * $13.53$: $\mathrm d \left({u v}\right) = u \ \mathrm d v + v \ \mathrm d u$


 * $13.54$: $\mathrm d \left({\dfrac u v}\right) = \dfrac{v \ \mathrm d u - u \ \mathrm d v} {v^2}$


 * $13.55$: $\mathrm d \left({u^n}\right) = n u^{n - 1} \ \mathrm d u$


 * $13.56$: $\mathrm d \left({\sin u}\right) = \cos u \ \mathrm d u$


 * $13.57$: $\mathrm d \left({\cos u}\right) = - \sin u \ \mathrm d u$