From 4b585ac13440e7a5bd7a5bc4dceb304c3c471bff Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= <anton@sijanec.eu>
Date: Thu, 6 Apr 2023 22:21:05 +0200
Subject: mat zadnji test, upam

---
 mat/test/odvodi.lyx | 412 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 412 insertions(+)
 create mode 100644 mat/test/odvodi.lyx

(limited to 'mat')

diff --git a/mat/test/odvodi.lyx b/mat/test/odvodi.lyx
new file mode 100644
index 0000000..01a1908
--- /dev/null
+++ b/mat/test/odvodi.lyx
@@ -0,0 +1,412 @@
+#LyX 2.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 544
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass article
+\begin_preamble
+\usepackage{siunitx}
+\usepackage{pgfplots}
+\usepackage{listings}
+\usepackage{multicol}
+\sisetup{output-decimal-marker = {,}, quotient-mode=fraction, output-exponent-marker=\ensuremath{\mathrm{3}}}
+\end_preamble
+\use_default_options true
+\maintain_unincluded_children false
+\language slovene
+\language_package default
+\inputencoding auto
+\fontencoding global
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification false
+\use_refstyle 1
+\use_minted 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\leftmargin 1cm
+\topmargin 0cm
+\rightmargin 1cm
+\bottommargin 2cm
+\headheight 1cm
+\headsep 1cm
+\footskip 1cm
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style german
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\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
-- 
cgit v1.2.3