Tabel turunan

Kelinearan

${\displaystyle \left({cf}\right)'=cf'}$

${\displaystyle \left({f+g}\right)'=f'+g'}$

Kaidah darab

${\displaystyle \left({fg}\right)'=f'g+fg'}$

Kaidah timbalbalik

${\displaystyle \left({\frac {1}{f}}\right)'={\frac {-f'}{f^{2}}},\qquad f\neq 0}$

Kaidah hasil-bagi

${\displaystyle \left({f \over g}\right)'={f'g-fg' \over g^{2}},\qquad g\neq 0}$

Kaidah rantai

${\displaystyle (f\circ g)'=(f'\circ g)g'}$

Turunan fungsi invers

${\displaystyle (f^{-1})'={\frac {1}{f'\circ f^{-1}}}}$

untuk setiap fungsi terdiferensialkan f dengan argumen riil dan dengan nilai riil, bila komposisi dan invers ada

Kaidah pangkat umum

${\displaystyle (f^{g})'=f^{g}\left(g'\ln f+{\frac {g}{f}}f'\right)}$

${\displaystyle c'=0\,}$

${\displaystyle x'=1\,}$

${\displaystyle (cx)'=c\,}$

${\displaystyle |x|'={x \over |x|}=\operatorname {sgn} x,\qquad x\neq 0}$

${\displaystyle (x^{c})'=cx^{c-1}\qquad {\mbox{baik }}x^{c}{\mbox{ maupun }}cx^{c-1}{\mbox{ terdefinisi}}}$

${\displaystyle \left({1 \over x}\right)'=\left(x^{-1}\right)'=-x^{-2}=-{1 \over x^{2}}}$

${\displaystyle \left({1 \over x^{c}}\right)'=\left(x^{-c}\right)'=-cx^{-(c+1)}=-{c \over x^{c+1}}}$

${\displaystyle \left({\sqrt {x}}\right)'=\left(x^{1 \over 2}\right)'={1 \over 2}x^{-{1 \over 2}}={1 \over 2{\sqrt {x}}},\qquad x>0}$

${\displaystyle \left(c^{x}\right)'=c^{x}\ln c,\qquad c>0}$

Perhatikan bahwa persamaan tersebut berlaku untuk semua c, namun turunan tersebut menghasilkan bilangan kompleks

${\displaystyle \left(e^{x}\right)'=e^{x}}$

${\displaystyle \left(^{c}\log x\right)'={\frac {1}{x\ln c}},\qquad c>0}$

${\displaystyle \left(\ln x\right)'={\frac {1}{x}}}$