Tabel turunan merupakan tabel yang menyenaraikan turunan fungsi-fungsi matematika . Operasi utama dalam kalkulus diferensial adalah mencari turunan fungsi . Dalam tabel berikut ini, f dan g adalah fungsi riil terturunkan, dan c adalah sebuah bilangan riil . Rumus-rumus berikut ini cukup untuk menurunkan fungsi elementer manapun.
Kaidah penurunan umum c ′ = 0 {\displaystyle c'=0\,} x ′ = 1 {\displaystyle x'=1\,} ( c x ) ′ = c {\displaystyle (cx)'=c\,} | x | ′ = x | x | = sgn x , x ≠ 0 {\displaystyle |x|'={x \over |x|}=\operatorname {sgn} x,\qquad x\neq 0} ( x c ) ′ = c x c − 1 baik x c maupun c x c − 1 terdefinisi {\displaystyle (x^{c})'=cx^{c-1}\qquad {\mbox{baik }}x^{c}{\mbox{ maupun }}cx^{c-1}{\mbox{ terdefinisi}}} ( 1 x ) ′ = ( x − 1 ) ′ = − x − 2 = − 1 x 2 {\displaystyle \left({1 \over x}\right)'=\left(x^{-1}\right)'=-x^{-2}=-{1 \over x^{2}}} ( 1 x c ) ′ = ( x − c ) ′ = − c x − ( c + 1 ) = − c x c + 1 {\displaystyle \left({1 \over x^{c}}\right)'=\left(x^{-c}\right)'=-cx^{-(c+1)}=-{c \over x^{c+1}}} ( x ) ′ = ( x 1 2 ) ′ = 1 2 x − 1 2 = 1 2 x , x > 0 {\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} ( sin x ) ′ = cos x {\displaystyle (\sin x)'=\cos x\,} ( arcsin x ) ′ = 1 1 − x 2 {\displaystyle (\arcsin x)'={1 \over {\sqrt {1-x^{2}}}}\,} ( cos x ) ′ = − sin x {\displaystyle (\cos x)'=-\sin x\,} ( arccos x ) ′ = − 1 1 − x 2 {\displaystyle (\arccos x)'={-1 \over {\sqrt {1-x^{2}}}}\,} ( tan x ) ′ = sec 2 x = 1 cos 2 x = 1 + tan 2 x {\displaystyle (\tan x)'=\sec ^{2}x={1 \over \cos ^{2}x}=1+\tan ^{2}x\,} ( arctan x ) ′ = 1 1 + x 2 {\displaystyle (\arctan x)'={1 \over 1+x^{2}}\,} ( sec x ) ′ = sec x tan x {\displaystyle (\sec x)'=\sec x\tan x\,} ( arcsec x ) ′ = 1 | x | x 2 − 1 {\displaystyle (\operatorname {arcsec} x)'={1 \over |x|{\sqrt {x^{2}-1}}}\,} ( csc x ) ′ = − csc x cot x {\displaystyle (\csc x)'=-\csc x\cot x\,} ( arccsc x ) ′ = − 1 | x | x 2 − 1 {\displaystyle (\operatorname {arccsc} x)'={-1 \over |x|{\sqrt {x^{2}-1}}}\,} ( cot x ) ′ = − csc 2 x = − 1 sin 2 x = − ( 1 + cot 2 x ) {\displaystyle (\cot x)'=-\csc ^{2}x={-1 \over \sin ^{2}x}=-(1+\cot ^{2}x)\,} ( arccot x ) ′ = − 1 1 + x 2 {\displaystyle (\operatorname {arccot} x)'={-1 \over 1+x^{2}}\,}
( sinh x ) ′ = cosh x = e x + e − x 2 {\displaystyle (\sinh x)'=\cosh x={\frac {e^{x}+e^{-x}}{2}}} ( arcsinh x ) ′ = 1 x 2 + 1 {\displaystyle (\operatorname {arcsinh} \,x)'={1 \over {\sqrt {x^{2}+1}}}} ( cosh x ) ′ = sinh x = e x − e − x 2 {\displaystyle (\cosh x)'=\sinh x={\frac {e^{x}-e^{-x}}{2}}} ( arccosh x ) ′ = 1 x 2 − 1 {\displaystyle (\operatorname {arccosh} \,x)'={1 \over {\sqrt {x^{2}-1}}}} ( tanh x ) ′ = sech 2 x {\displaystyle (\tanh x)'=\operatorname {sech} ^{2}\,x} ( arctanh x ) ′ = 1 1 − x 2 {\displaystyle (\operatorname {arctanh} \,x)'={1 \over 1-x^{2}}} ( sech x ) ′ = − tanh x sech x {\displaystyle (\operatorname {sech} \,x)'=-\tanh x\,\operatorname {sech} \,x} ( arcsech x ) ′ = − 1 x 1 − x 2 {\displaystyle (\operatorname {arcsech} \,x)'={-1 \over x{\sqrt {1-x^{2}}}}} ( csch x ) ′ = − coth x csch x {\displaystyle (\operatorname {csch} \,x)'=-\,\operatorname {coth} \,x\,\operatorname {csch} \,x} ( arccsch x ) ′ = − 1 | x | 1 + x 2 {\displaystyle (\operatorname {arccsch} \,x)'={-1 \over |x|{\sqrt {1+x^{2}}}}} ( coth x ) ′ = − csch 2 x {\displaystyle (\operatorname {coth} \,x)'=-\,\operatorname {csch} ^{2}\,x} ( arccoth x ) ′ = 1 1 − x 2 {\displaystyle (\operatorname {arccoth} \,x)'={1 \over 1-x^{2}}}
Turunan fungsi khusus 
