eMathematician
Forums
Formulary
Log in Sign up
       
« HomeCalculus33

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.
$$\begin{array}{|c|c|}
\hline
  \ \ \ \ \ f(x) \ \ \ \ \ & \ \ \ \ \ f'(x) \ \ \ \ \ \\\hline
  c & 0 \\\hline
  x & 1 \\\hline
  cx & c \\\hline
  x^a & ax^{a-1} \\\hline
  \sqrt{x} & \frac{1}{2\sqrt{x}} \\\hline
  {a^x} & a^x \ln a \\\hline
  {e^x} & e^x \\\hline
  \log_ax & \frac{1}{x\cdot \ln a} \\\hline
  \ln x & \frac{1}{x} \\\hline
  \sin x & \cos x \\\hline
  \cos x & -\sin x \\\hline
  \text{tg} \ x & \frac{1}{\cos^2x} \\\hline
  \text{ctg} \ x & -\frac{1}{\sin^2x} \\\hline
  \text{arcsin} \ x & \frac{1}{\sqrt{1-x^2}} \\\hline
  \text{arccos} \ x & -\frac{1}{\sqrt{1-x^2}} \\\hline
  \text{arctg} \ x & \frac{1}{1+x^2} \\\hline
  \text{arcctg} \ x & -\frac{1}{1+x^2} \\\hline
\end{array}$$

0

If you want to write answers, you have to login!