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\begin_layout Title Osnovni izreki začetka analize \end_layout \begin_layout Author \noun on Anton Luka Šijanec \end_layout \begin_layout Date \begin_inset ERT status open \begin_layout Plain Layout \backslash today \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash newcommand \backslash euler{e} \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{multicols}{2} \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ \frac{df}{dx}=f'(x_{0})=\lim_{h\to0}\frac{f(x_{0}+h)-f(x_{0})}{h}=\tan\varphi \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ (f(x)+g(x))'=f'(x)+g'(x) \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ (f(x)\cdot g(x))'=f'(x)\cdot g(x)+f(x)\cdot g'(x) \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ (c\cdot f(x))'=c\cdot f'(x) \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ \left(\frac{f(x)}{g(x)}\right)'=\frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{g^{2}(x)} \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ p\perp q\Rightarrow k_{p}=-k_{q}^{-1}\ ;\ \ \ p\parallel q\Rightarrow k_{p}=k_{q} \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ (x^{r})'=r\cdot x^{r-1},x\in\mathbb{R} \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ \tan\varphi=\lvert\frac{k_{2}-k_{1}}{1+k_{2}k_{1}}\rvert \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ (g\circ f)'(x)=\left[g(f(x))\right]'=g(f(x))'\cdot f'(x) \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ (f^{-1}(x))'=\frac{-1}{f'(f^{-1}(x))} \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ \sin\alpha-\sin\beta=2\sin\frac{\alpha-\beta}{2}\cdot\cos\frac{\alpha+\beta}{2} \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ \lim_{x\to0}\frac{\sin x}{x}=1;\ \sin^{2}x+\cos^{2}x=1 \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ \sin'x=\cos'x;\ cos'x=-\sin x;\ \tan'x=\cos^{-2}x;\ \cot'x=-\sin^{-2}x \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ 1+\tan^{2}x=cos^{-2}x;\ 1+\cot^{2}x=\sin^{-2}x \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ \arcsin'x=\frac{1}{\sqrt{1-x^{2}}}=-\arccos'x;\ \arctan'x=\frac{1}{1+x^{2}}=-\text{arccot}'x \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ \log_{a}(bc)=\log_{a}b+\log_{a}c;\ log_{a}b^{r}=r\cdot\log_{a}b;\ \log_{a}x=\frac{\log_{b}x}{\log_{b}a} \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ y=log_{a}x\Leftrightarrow x=a^{b};\ x=a^{\log_{a}x} \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ \lim_{\lvert t\rvert\to\infty}\left(1+t^{-1}\right)^{t}=\euler;\ t\ensuremath{\in\mathbb{R}} \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ \left(\log_{a}x\right)'=\frac{\log_{a}\euler}{x}=\frac{1}{x\cdot\ln a};\ \left(\ln x\right)'=x^{-1} \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ (a^{x})'=a^{x}\ln a\Rightarrow(\euler^{x})'=\euler^{x} \] \end_inset \end_layout \begin_layout Standard \begin_inset Formula \[ f(x_{0}+h)\approx f(x_{0})+f'(x_{0})\cdot h \] \end_inset \end_layout \begin_layout Standard \end_layout \begin_layout Standard Za možne napake ne odgovarjam. Vse te izreke najdemo v učbeniku. Srečno! \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash end{multicols} \end_layout \end_inset \end_layout \end_body \end_document