Ogled vira Tabela odvodov

[[Odvod]] je osnovna operacija infinitezimalnega računa. Spodaj so navedena najpomembnejša pravila za odvajanje.

=== Pravila za sestavljanje funkcije ===
:{| style="text-align: center; width: 75%; margin: 0 auto; border-collapse: collapse" border="1" cellpadding="4" cellspacing="1"
|-style="background: #AABBCC;"
!width="40%"|funkcija
!width="30%"|odvod
!width="30%"|opombe
|-
| <math>f \pm g</math>
| <math>f' \pm g'</math>
|
|-
| <math>c \cdot f</math>
| <math>c \cdot f'</math>
| ''c'' je konstanta
|-
| <math>f \cdot g</math>
| <math>f' \cdot g + f \cdot g'</math>
| [[odvod produkta]]
|-
| <math>{f \over g}</math>
| <math>{{f' \cdot g - f \cdot g'} \over g^2}</math>
| <math> g \ne 0 </math> <br /> [[odvod kvocienta]]
|-
| <math>f \circ g = f(g)</math>
| <math>(f^{\prime} \circ g) \cdot g' = f'(g) \cdot g'</math>
|
|}

===Odvodi elementarnih funkcij===
:{| style="text-align: center; width: 75%; margin: 0 auto; border-collapse: collapse" border="1" cellpadding="4" cellspacing="1"
|-style="background: #AABBCC;"
!width="40%"|Funkcija
!width="30%"|Odvod
!width="30%"|Opombe
|-
| <math>c\!\,</math>
| <math>0\!\,</math>
| <math>c \in \mathbb R</math>
|-
| <math>x\!\,</math>
| <math>1\!\,</math>
|
|-
| <math>x^n\!\,</math>
| <math>nx^{n-1}\!\,</math>
| <math>n \in \mathbb{R} </math>
|-
| <math>1 \over x</math>
| <math>-{1 \over x^2}</math>
| <math>x\ne 0\!\,</math>
|-
|<math>1 \over x^2</math>
|<math>-{2 \over x^3}</math>
|<math>x\ne 0\!\,</math>
|-
| <math>\sqrt x</math>
| <math>1 \over 2 \sqrt x</math>
| <math>x>0\!\,</math>
|-
| <math>\sqrt[n] x</math>
| <math>1 \over n \sqrt[n]{x^{n-1}}</math>
| <math>x>0\!\,</math>
|-
| <math>\sin x\!\,</math>
| <math>\cos x\!\,</math>
|
|-
|<math>\sin (ax)</math>
|<math>a \cos (a x)</math>
|
|-
| <math>\cos x\!\,</math>
| <math>-\sin x\!\,</math>
|
|-
|<math>\cos (a x)</math>
|<math>-a \sin (a x)</math>
|
|-
| <math>\tan x</math>
| <math>1 \over \cos^2 x</math>
| <math>x \ne {\pi \over 2}+k\pi,\; k \in \mathbb Z</math>
|-
| <math>\cot x</math>
| <math>-{1 \over \sin^2 x}</math>
| <math>x\ne k\pi,\; k \in \mathbb Z</math>
|-
| <math>e^x\!\,</math>
| <math>e^x\!\,</math>
|
|-
|<math>e^k\!\,^x</math>
|<math>ke^k\!\,^x</math>
|
|-
| <math>a^x\!\,</math>
| <math>a^x \ln a\!\,</math>
| <math>a>0\!\,</math>
|-
| <math>x^x\!\,</math>
| <math>x^x (1+\ln x)\!\,</math>
| <math>x>0\!\,</math>
|-
| <math>\ln x\!\,</math>
| <math>1 \over x</math>
| <math>x>0\!\,</math>
|-
| <math>\log_a x\!\,</math>
| <math>1 \over x\ln a</math>
| <math>a>0,~~ x>0\!\,</math>
|-
| <math>\arcsin x</math>
| <math>1 \over \sqrt {1 - x^2}</math>
| <math>|x|<1\!\,</math>
|-
| <math>\arccos x</math>
| <math>-{1 \over \sqrt{1 - x^2}}</math>
|<math>|x|<1\!\,</math>
|-
| <math>\arctan x</math>
| <math>1 \over 1 + x^2</math>
|
|- align="center"
| <math>\operatorname{arccot}x</math>
| <math>-{1 \over 1 + x^2}</math>
|
|-
| <math>\operatorname{sh}x = {{e^x - e^{-x}} \over 2}</math>
| <math>\operatorname{ch}x = {{e^x + e^{-x}} \over 2}</math>
|
|-
| <math>\operatorname{ch}x = {{e^x + e^{-x}} \over 2}</math>
| <math>\operatorname{sh}x = {{e^x - e^{-x}} \over 2}</math>
|
|-
| <math>\operatorname{th}x = {\operatorname{sh}x \over \operatorname{ch}x}</math>
| <math>{1 \over \operatorname{ch}^2x} = {4 \over ({e^x + e^{-x}})^2}</math>
|
|-
| <math>\operatorname{arth}x = {1 \over 2}\ln {1+x \over 1-x}</math>
| <math>1 \over 1-x^2</math>
|<math>|x|<1\!\,</math>
|-
|<math>\ln (x+\sqrt{x^2 \pm a^2})</math>
|<math>1 \over \sqrt{x^2 \pm a^2}</math>
|
|}

== Glej tudi ==

* [[odvod]]
* [[pravila odvajanja]]
* [[Tabela integralov]]

[[Kategorija:Infinitezimalni račun]]
[[Kategorija:Pravila odvajanja]]

[[bs:Tablica izvoda]]
[[en:List of differentiation identities]]
[[es:Tabla de derivadas]]
[[pl:Pochodna funkcji#Pochodne_funkcji_elementarnych]]