Tabela Odvodov

Spodaj so navedena najpomembnejša pravila za odvajanje.

Pravila za sestavljanje funkcije

funkcija	odvod	opombe
${\displaystyle f\pm g}$	${\displaystyle f'\pm g'}$
${\displaystyle c\cdot f}$	${\displaystyle c\cdot f'}$	c je konstanta
${\displaystyle f\cdot g}$	${\displaystyle f'\cdot g+f\cdot g'}$	odvod produkta
${\displaystyle {f \over g}}$	${\displaystyle {{f'\cdot g-f\cdot g'} \over g^{2}}}$	${\displaystyle g\neq 0}$ odvod kvocienta
${\displaystyle f\circ g=f(g)}$	${\displaystyle (f^{\prime }\circ g)\cdot g'=f'(g)\cdot g'}$

Odvodi elementarnih funkcij

Funkcija	Odvod	Opombe
${\displaystyle c\!\,}$	${\displaystyle 0\!\,}$	${\displaystyle c\in \mathbb {R} }$
${\displaystyle x\!\,}$	${\displaystyle 1\!\,}$
${\displaystyle x^{n}\!\,}$	${\displaystyle nx^{n-1}\!\,}$	${\displaystyle n\in \mathbb {R} }$
${\displaystyle 1 \over x}$	${\displaystyle -{1 \over x^{2}}}$	${\displaystyle x\neq 0\!\,}$
${\displaystyle 1 \over x^{2}}$	${\displaystyle -{2 \over x^{3}}}$	${\displaystyle x\neq 0\!\,}$
${\displaystyle {\sqrt {x}}}$	${\displaystyle 1 \over 2{\sqrt {x}}}$	${\displaystyle x>0\!\,}$
${\displaystyle {\sqrt[{n}]{x}}}$	${\displaystyle 1 \over n{\sqrt[{n}]{x^{n-1}}}}$	${\displaystyle x>0\!\,}$
${\displaystyle \sin x\!\,}$	${\displaystyle \cos x\!\,}$
${\displaystyle \sin(ax)}$	${\displaystyle a\cos(ax)}$
${\displaystyle \cos x\!\,}$	${\displaystyle -\sin x\!\,}$
${\displaystyle \cos(ax)}$	${\displaystyle -a\sin(ax)}$
${\displaystyle \tan x}$	${\displaystyle 1 \over \cos ^{2}x}$	${\displaystyle x\neq {\pi \over 2}+k\pi ,\;k\in \mathbb {Z} }$
${\displaystyle \cot x}$	${\displaystyle -{1 \over \sin ^{2}x}}$	${\displaystyle x\neq k\pi ,\;k\in \mathbb {Z} }$
${\displaystyle e^{x}\!\,}$	${\displaystyle e^{x}\!\,}$
${\displaystyle e^{k}\!\,^{x}}$	${\displaystyle ke^{k}\!\,^{x}}$
${\displaystyle a^{x}\!\,}$	${\displaystyle a^{x}\ln a\!\,}$	${\displaystyle a>0\!\,}$
${\displaystyle x^{x}\!\,}$	${\displaystyle x^{x}(1+\ln x)\!\,}$	${\displaystyle x>0\!\,}$
${\displaystyle \ln x\!\,}$	${\displaystyle 1 \over x}$	${\displaystyle x>0\!\,}$
${\displaystyle \log _{a}x\!\,}$	${\displaystyle 1 \over x\ln a}$	${\displaystyle a>0,~~x>0\!\,}$
${\displaystyle \arcsin x}$	${\displaystyle 1 \over {\sqrt {1-x^{2}}}}$	${\displaystyle |x|<1\!\,}$
${\displaystyle \arccos x}$	${\displaystyle -{1 \over {\sqrt {1-x^{2}}}}}$	${\displaystyle |x|<1\!\,}$
${\displaystyle \arctan x}$	${\displaystyle 1 \over 1+x^{2}}$
${\displaystyle \operatorname {arccot} x}$	${\displaystyle -{1 \over 1+x^{2}}}$
${\displaystyle \operatorname {sh} x={{e^{x}-e^{-x}} \over 2}}$	${\displaystyle \operatorname {ch} x={{e^{x}+e^{-x}} \over 2}}$
${\displaystyle \operatorname {ch} x={{e^{x}+e^{-x}} \over 2}}$	${\displaystyle \operatorname {sh} x={{e^{x}-e^{-x}} \over 2}}$
${\displaystyle \operatorname {th} x={\operatorname {sh} x \over \operatorname {ch} x}}$	${\displaystyle {1 \over \operatorname {ch} ^{2}x}={4 \over ({e^{x}+e^{-x}})^{2}}}$
${\displaystyle \operatorname {arth} x={1 \over 2}\ln {1+x \over 1-x}}$	${\displaystyle 1 \over 1-x^{2}}$	${\displaystyle |x|<1\!\,}$
${\displaystyle \ln(x+{\sqrt {x^{2}\pm a^{2}}})}$	${\displaystyle 1 \over {\sqrt {x^{2}\pm a^{2}}}}$

• odvod
• pravila odvajanja
• Tabela integralov