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: $\map {\dfrac \d {\d x} } {u \pm v \pm w \pm \cdots}$

$13.6$: 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: $\dfrac {\d y} {\d x} = \dfrac {\d y} {\d u} \dfrac {\d u} {\d x}$

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

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