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.
 * $13.52$: $\map \d {u \pm v \pm w \cdots} = \d u \pm \d v \pm \d w \pm \cdots$


 * $13.53$: $\map \d {u v} = u \rd v + v \rd u$


 * $13.54$: $\map \d {\dfrac u v} = \dfrac {v \rd u - u \rd v} {v^2}$


 * $13.55$: $\map \d {u^n} = n u^{n - 1} \rd u$


 * $13.56$: $\map \d {\sin u} = \cos u \rd u$


 * $13.57$: $\map \d {\cos u} = -\sin u \rd u$