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