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

General Rules of Differentiation
In the following, $u, v, w$ are functions of $x$; $a, b, c, n$ any constants, restricted if indicated; $e = 2.71828 \ldots$ is the natural base of logarithms; $\ln u$ denotes the natural logarithm of $u$ where it is assumed that $u > 0$ and all angles are in radians.


 * $13.2$: Derivative of $c$


 * $13.3$: Derivative of $c x$


 * $13.4$: Derivative of $c x^n$


 * $13.5$: Derivative of Sum of Functions: $\dfrac {\mathrm d} {\mathrm d x} \left({u \pm v \pm w \pm \cdots}\right)$


 * $13.6$: Derivative of $c u$


 * $13.7$: Derivative of $u v$


 * $13.8$: Derivative of $u v w$


 * $13.9$: Derivative of $\dfrac u v$


 * $13.10$: Derivative of $u^n$


 * $13.11$: Chain rule: $\dfrac {\mathrm d y} {\mathrm d x} = \dfrac {\mathrm d y} {\mathrm d u} \dfrac {\mathrm d u} {\mathrm d x}$


 * $13.12$: Derivative of Inverse Function: $\dfrac {\mathrm d u} {\mathrm d x} = \dfrac 1 {\mathrm d x / \mathrm d u}$


 * $13.13$: Corollary of Chain Rule: $\dfrac {\mathrm d y} {\mathrm d x} = \dfrac {\mathrm d y / \mathrm d u} {\mathrm d x / \mathrm d u}$