| Funcţia | Derivata funcţiei | Domeniul derivatei |
| \(f(x)=c,\:c\in\mathbf{R}\) | \(f'(x)=0\) | \(\mathbf{R}\) |
| \(f(x)=x^{n},\:n\in\mathbf{N}^{*}\) | \(f'(x)=nx^{n-1}\) | \(\mathbf{R}\) |
| \(f(x)=x^{a},\:a\in\mathbf{R}\) | \(f'(x)=ax^{a-1}\) | \(\mathbf{R}\) |
| \(f(x)=\sqrt{x}\) | \(f'(x)=\frac{1}{2\sqrt{x}}\) | \((0,+\infty)\) |
| \(f(x)=\log_{a}x\) | \(f'(x)=\frac{1}{x\ln a}\) | \((0,+\infty)\) |
| \(f(x)=\ln{x}\) | \(f'(x)=\frac{1}{x}\) | \((0,+\infty)\) |
| \(f(x)=a^{x},\:a>0,\: a\neq 0\) | \(f'(x)=a^{x}\ln{a}\) | \(\mathbf{R}\) |
| \(f(x)=\sin{x}\) | \(f'(x)=\cos{x}\) | \(\mathbf{R}\) |
| \(f(x)=\cos{x}\) | \(f'(x)=-\sin{x}\) | \(\mathbf{R}\) |
| \(f(x)=tgx\) | \(f'(x)=\frac{1}{\cos^{2}{x}}\) | \(\mathbf{R}-\left\{ \frac{\pi}{2}+k\pi|k\in\mathbf{Z}\right\}\) |
| \(f(x)=\arcsin x\) | \(f'(x)=\frac{1}{\sqrt[]{1-x^{2}}}\) | \((-1,1)\) |
| \(f(x)=\arccos x\) | \(f'(x)=-\frac{1}{\sqrt[]{1-x^{2}}}\) | \((-1,1)\) |
| \(f(x)=arctg\;x\) | \(f'(x)=\frac{1}{1+x^{2}}\) | \(\mathbf{R}\) |
| \(f(x)=arcctg\;x\) | \(f'(x)=-\frac{1}{1+x^{2}} \) | \(\mathbf{R}\) |