### Derivatele funcţiilor elementare

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