Primarna operacija u diferencijalnom kalkulusu je računanje derivacije. Ova tabela sadrži derivacije nekih osnovnih funkcija. U sljedećem tekstu, f i g su diferencijabilne funkciju u skupu realnih brojeva, a c je realan broj. Ove formule su dovoljne za izračunavanje derivacija bilo koje elementarne funkcije.
- Linearnost
![{\displaystyle \left({cf}\right)'=cf'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/39da2451f330fae32b6ba571000d159d36cb0c46)
![{\displaystyle \left({f+g}\right)'=f'+g'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a356fcc9b7f291689d9de9086dd2fc12ed1af479)
![{\displaystyle \left({f-g}\right)'=f'-g'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bd4684ab43bc960df5b488f4b3ae3e7498c5e7f3)
- Pravilo derivacije proizvoda
![{\displaystyle \left({fg}\right)'=f'g+fg'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b087f14a89a896de41077c78ad39da0a56412e97)
- Pravilo derivacije količnika
![{\displaystyle \left({f \over g}\right)'={f'g-fg' \over g^{2}},\qquad g\neq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a31aa870daebebcde7a311f0e0e536ec749fa04)
- Pravilo derivacije funkcije sa potencijom
![{\displaystyle (f^{g})'=\left(e^{g\ln f}\right)'=f^{g}\left(f'{g \over f}+g'\ln f\right),\qquad f>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/feb836eb3b15bb62ef6285cc4a1c45a131f9a5d6)
- Pravilo derivacije složene funkcije
![{\displaystyle (f\circ g)'=(f'\circ g)g'}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5b8f37ab4032a1466a59d9f3c70e2e669bc5b560)
- Pravilo derivacije logaritma
![{\displaystyle f'=(\ln f)'f,\qquad f>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/082afa7ba15f154703f9e8b9c86db31fb9511165)
Derivacije jednostavnih funkcija[uredi | uredi izvor]
![{\displaystyle {d \over dx}c=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4d66384c0fe25d80d440b317f08c9b8be9253e77)
![{\displaystyle {d \over dx}x=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/03e3d9ed50d0216e5b16c4827596e3fdcc2deacb)
![{\displaystyle {d \over dx}cx=c}](https://wikimedia.org/api/rest_v1/media/math/render/svg/867347efd790e06d7298f9a61aea5041e41fb86d)
![{\displaystyle {d \over dx}|x|={|x| \over x}=\operatorname {sgn} x,\qquad x\neq 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/350ec1c5235e07d0aaa3ffadbf597273a1caf291)
![{\displaystyle {d \over dx}x^{c}=cx^{c-1}\qquad {\mbox{gdje su i }}x^{c}{\mbox{ i }}cx^{c-1}{\mbox{ definisane}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/89ab268a511bedf91de02e49d5bec3710c491aeb)
![{\displaystyle {d \over dx}\left({1 \over x}\right)={d \over dx}\left(x^{-1}\right)=-x^{-2}=-{1 \over x^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e841696967b58af8cc0eb528e604a7df0e52cdbd)
![{\displaystyle {d \over dx}\left({1 \over x^{c}}\right)={d \over dx}\left(x^{-c}\right)=-{c \over x^{c+1}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5608969750f40ea606c7dea0f257c76014f81895)
![{\displaystyle {d \over dx}{\sqrt {x}}={d \over dx}x^{1 \over 2}={1 \over 2}x^{-{1 \over 2}}={1 \over 2{\sqrt {x}}},\qquad x>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4db5a7c70c791c69e9f8c4591bd3765fd2cf723c)
![{\displaystyle {d \over dx}c^{x}={c^{x}\ln c},\qquad c>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d595b56138acbd74c00aae36d407fe71f3b2dd7c)
![{\displaystyle {d \over dx}e^{x}=e^{x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a2528d3e349a763e4afd73cddc3ec599ffca15e4)
![{\displaystyle {d \over dx}\log _{c}x={1 \over x\ln c},\qquad c>0,c\neq 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2456ba331f9193749358238ae80a51a579b1bff6)
![{\displaystyle {d \over dx}\ln x={1 \over x},\qquad x>0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13505ad13a957d585995644a78568fe7e7b9c398)
![{\displaystyle {d \over dx}\ln |x|={1 \over x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41ee002e46c6ad508619d162d8c484ee5637e265)
![{\displaystyle {d \over dx}x^{x}=x^{x}(1+\ln x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/46c2c2e041b4a0a9bcc2549f422a7134def94e97)
![{\displaystyle {d \over dx}\sin x=\cos x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c976bcdb6b29573bc73f234a44acd4f9bb3ea8d3)
![{\displaystyle {d \over dx}\cos x=-\sin x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2dbeeef651fc6d4f1515c348981a99f97e5d9ab3)
![{\displaystyle {d \over dx}\tan x=\sec ^{2}x={1 \over \cos ^{2}x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eecb39df5f14e2474ae267284a6e0147f5edfb33)
![{\displaystyle {d \over dx}\sec x=\tan x\sec x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2f114356317ff48490ac235e8d69edb95e564547)
![{\displaystyle {d \over dx}\cot x=-\csc ^{2}x={-1 \over \sin ^{2}x}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/88e65088665af3331b4797ba4415050312498a6b)
![{\displaystyle {d \over dx}\csc x=-\csc x\cot x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/09258cdb5b76231c39367662468a13babd56c74c)
![{\displaystyle {d \over dx}\arcsin x={1 \over {\sqrt {1-x^{2}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3695240e676e214b65661196c477a8d06ad25145)
![{\displaystyle {d \over dx}\arccos x={-1 \over {\sqrt {1-x^{2}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/694f1f1ec9823b1af7a76c435f1be1b8150536a4)
![{\displaystyle {d \over dx}\arctan x={1 \over 1+x^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2ffbeab56eb8ceb4a7bd93e7341b6a45170ba0ab)
![{\displaystyle {d \over dx}\operatorname {arcsec} x={1 \over |x|{\sqrt {x^{2}-1}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/42da001ad7ea996603263d152a9479be330dafd3)
![{\displaystyle {d \over dx}\operatorname {arccot} x={-1 \over 1+x^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6e67da0f756cdcf3ace4c4f2fc64f822b4b5a40d)
![{\displaystyle {d \over dx}\operatorname {arccsc} x={-1 \over |x|{\sqrt {x^{2}-1}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/15a59301aa2b9bd7d3c24012712d119ae367bf4b)
![{\displaystyle {d \over dx}\sinh x=\cosh x={\frac {e^{x}+e^{-x}}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dfd585210df2d572ee69b2d0decca68d60532641)
![{\displaystyle {d \over dx}\cosh x=\sinh x={\frac {e^{x}-e^{-x}}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/62e82be1ab0ae8912f87d0edb4ad40ed3e0fe6a8)
![{\displaystyle {d \over dx}\tanh x=\operatorname {sech} ^{2}\,x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5a56722a21abd43b5eeddcc7744d8c31e97ae539)
![{\displaystyle {d \over dx}\,\operatorname {sech} \,x=-\tanh x\,\operatorname {sech} \,x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/28880630ee4e456ecbc143a9b123e4705eeb42e3)
![{\displaystyle {d \over dx}\,\operatorname {coth} \,x=-\,\operatorname {csch} ^{2}\,x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/64ceb55e3a64e4aba52689b1be832a22e2900f16)
![{\displaystyle {d \over dx}\,\operatorname {csch} \,x=-\,\operatorname {coth} \,x\,\operatorname {csch} \,x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/238fb46cafcce56060527323df58700a51db119a)
![{\displaystyle {d \over dx}\,\operatorname {arcsinh} \,x={1 \over {\sqrt {x^{2}+1}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/789104eecbf1e0a1862d0a8a54756fd4c92c967a)
![{\displaystyle {d \over dx}\,\operatorname {arccosh} \,x={1 \over {\sqrt {x^{2}-1}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe4c92e415b1105ce4f0520e0c0e8ed59a159a47)
![{\displaystyle {d \over dx}\,\operatorname {arctanh} \,x={1 \over 1-x^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7fcf6ba7ee2f290bc1d1ad13386ad085634358cb)
![{\displaystyle {d \over dx}\,\operatorname {arcsech} \,x={-1 \over x{\sqrt {1-x^{2}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/88e04b2d1c4c3fff12a7878bd16dcd1494ed2d8d)
![{\displaystyle {d \over dx}\,\operatorname {arccoth} \,x={1 \over 1-x^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/70f67ea12ad2b5bb503f08fb71d1a0879adb6ce3)
![{\displaystyle {d \over dx}\,\operatorname {arccsch} \,x={-1 \over |x|{\sqrt {1+x^{2}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b42282ca2264d3622eb50d9e6db94d8edfafc86f)