# Table of Derivatives Formulas

$$c’=0,\quad c=const;$$

$$(x^\alpha)’=\alpha x^{\alpha-1}, \quad x\in \mathbb{R}, \alpha\in \mathbb{R};$$

$$(a^x)’=a^x\ln a,\quad a>0, a\neq 1, x\in \mathbb{R};$$

$$(e^x)’=e^x;$$

$$(\log_a x)’=\frac{1}{x\ln a}, \quad x>0;$$

$$(\log_a|x|)’=\frac{1}{x\ln a},\quad x\neq 0;$$

$$(\ln x)’=\frac{1}{x},\quad x>0;$$

$$(\sin x)’=\cos x, \quad x\in \mathbb{R};$$

$$(\cos x)’=-\sin x\quad x\in \mathbb{R};$$

$$(\mathrm{tg} x)’=\frac{1}{\cos^2 x},\quad x\neq \frac{\pi}{2}(2n+1), n\in \mathbb{Z};$$

$$(\mathrm{ctg} x)’=-\frac{1}{\sin^2 x},\quad x\neq \pi n, n\in \mathbb{Z};$$

$$(\arcsin x)’=\frac{1}{\sqrt{1-x^2}},\quad |x|<1;$$

$$(\arccos x)’=-\frac{1}{\sqrt{1-x^2}},\quad |x|<1;$$

$$(\mathrm{arctg} x)’=\frac{1}{1+x^2},\quad x\in\mathbb{R};$$

$$(\mathrm{arcctg} x)’=-\frac{1}{1+x^2},\quad x\in\mathbb{R};$$

$$(\mathrm{sh} x)’=\mathrm{ch} x, \quad x\in \mathbb{R};$$

$$(\mathrm{ch} x)’=\mathrm{sh} x\quad x\in \mathbb{R};$$

$$(\mathrm{th} x)’=\frac{1}{\mathrm{ch}^2 x},\quad x\neq \frac{\pi}{2}(2n+1), n\in \mathbb{Z};$$

$$(\mathrm{cth} x)’=-\frac{1}{\mathrm{sh}^2 x},\quad x\neq \pi n, n\in \mathbb{Z};$$

$$(\mathrm{arsh} x)’=\frac{1}{\sqrt{x^2+1}},\quad x\in\mathbb{R};$$

$$(\mathrm{arch} x)’=-\frac{1}{\sqrt{x^2-1}},\quad |x|>1;$$

$$(\mathrm{arth} x)’=\frac{1}{1-x^2},\quad x\in\mathbb{R};$$