| Функция \( f(x) \) | Производная \( f'(x) \) |
| \( C \) (константа) | 0 |
| \( x^n \) | \( nx^{n-1} \) |
| \( \frac{1}{x} \) | \( -\frac{1}{x^2} \) |
| \( \sqrt{x} \) | \( \frac{1}{2\sqrt{x}} \) |
| \( a^x \) | \( a^x \ln{a} \) |
| \( e^x \) | \( e^x \) |
| \( \log_a{x} \) | \( \frac{1}{x \ln{a}} \) |
| \( \ln{x} \) | \( \frac{1}{x} \) |
| \( \sin{x} \) | \( \cos{x} \) |
| \( \cos{x} \) | \( -\sin{x} \) |
| \( \tan{x} \) | \( \frac{1}{\cos^2{x}} \) |
| \( \cot{x} \) | \( -\frac{1}{\sin^2{x}} \) |