# Basic formulas and rules of calculating derivatives

Common rules of calculating derivatives: multiplication by constant, sum and difference, product and quotient rules.
$$(c\cdot u)'=c\cdot u', \ (u \pm v)'=u' \pm v'$$ $$(u\cdot v)'=u'\cdot v + u\cdot v' \\ \left(\frac{u}{v}\right)'=\frac{u'\cdot v-u\cdot v'}{v^2}$$
Common functions and their derivatives table.
$$\begin{array}{|c|c|} \hline \ \ \ \ \ f(x) \ \ \ \ \ & \ \ \ \ \ f'(x) \ \ \ \ \ \\\hline c & 0 \\\hline x & 1 \\\hline cx & c \\\hline x^a & ax^{a-1} \\\hline \sqrt{x} & \frac{1}{2\sqrt{x}} \\\hline {a^x} & a^x \ln a \\\hline {e^x} & e^x \\\hline \log_ax & \frac{1}{x\cdot \ln a} \\\hline \ln x & \frac{1}{x} \\\hline \sin x & \cos x \\\hline \cos x & -\sin x \\\hline \text{tg} \ x & \frac{1}{\cos^2x} \\\hline \text{ctg} \ x & -\frac{1}{\sin^2x} \\\hline \text{arcsin} \ x & \frac{1}{\sqrt{1-x^2}} \\\hline \text{arccos} \ x & -\frac{1}{\sqrt{1-x^2}} \\\hline \text{arctg} \ x & \frac{1}{1+x^2} \\\hline \text{arcctg} \ x & -\frac{1}{1+x^2} \\\hline \end{array}$$

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