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.
Informasi lebih lanjut Kalkulus, Definisi ...
Tutup
![{\displaystyle c'=0\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/6981c5664efd12d89a3b2701c946b1f58c07bdca)
![{\displaystyle x'=1\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/9b941386f28d58bf7bf927c9fe0b5a3133e65d2d)
![{\displaystyle (cx)'=c\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/6dafb034766ceb5e8bf54ec720e0b436ce919b02)
![{\displaystyle |x|'={x \over |x|}=\operatorname {sgn} x,\qquad x\neq 0}](//wikimedia.org/api/rest_v1/media/math/render/svg/29a45d7d3ce4594e45569d18b4691a4aa5dd1d05)
![{\displaystyle (x^{c})'=cx^{c-1}\qquad {\mbox{baik }}x^{c}{\mbox{ maupun }}cx^{c-1}{\mbox{ terdefinisi}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/ea0f36a9ed37c91efb9cc4643dd5f54607cf9ed2)
![{\displaystyle \left({1 \over x}\right)'=\left(x^{-1}\right)'=-x^{-2}=-{1 \over x^{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/fa4b96aa6d2a5389cfd54bdff232abdf75d21329)
![{\displaystyle \left({1 \over x^{c}}\right)'=\left(x^{-c}\right)'=-cx^{-(c+1)}=-{c \over x^{c+1}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/8fdf93b0e22f208503294f2cbcceebbd8fdc3aac)
![{\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}](//wikimedia.org/api/rest_v1/media/math/render/svg/d479bf920c3f2e702d7e22a61f4b4778ccfb9cf4)
![{\displaystyle (\sin x)'=\cos x\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/0a15ba1cb701e9708cacdb018cf1755f56ef6efa) |
![{\displaystyle (\arcsin x)'={1 \over {\sqrt {1-x^{2}}}}\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/c1e2d812fca707e0ad1c48d023dd728f44288526) |
![{\displaystyle (\cos x)'=-\sin x\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/8855b905f39e51b4a63980de3a9663cba6970d55) |
![{\displaystyle (\arccos x)'={-1 \over {\sqrt {1-x^{2}}}}\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/382db41eef46814df52c409f0344d281dbd2be6c) |
![{\displaystyle (\tan x)'=\sec ^{2}x={1 \over \cos ^{2}x}=1+\tan ^{2}x\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/df08cdd79d004810f85a136324a8c02bc26cdf8a) |
![{\displaystyle (\arctan x)'={1 \over 1+x^{2}}\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/8df7435e56644e257e6aff4eb9b327722bf109cb) |
![{\displaystyle (\sec x)'=\sec x\tan x\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/c63db950fa9914c618ff1ec482386f4d5fef896a) |
![{\displaystyle (\operatorname {arcsec} x)'={1 \over |x|{\sqrt {x^{2}-1}}}\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/5a11aeac6db521c16e120b202bdafcfa31303727) |
![{\displaystyle (\csc x)'=-\csc x\cot x\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/ed929106cbc77ca3126a54cbc956316475b4d012) |
![{\displaystyle (\operatorname {arccsc} x)'={-1 \over |x|{\sqrt {x^{2}-1}}}\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/4eb3a00a2821f5e6bda347e55f6014c9d0602ddc) |
![{\displaystyle (\cot x)'=-\csc ^{2}x={-1 \over \sin ^{2}x}=-(1+\cot ^{2}x)\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/0ea499fd01b8ca32364b8d4a8756b037749ea391) |
![{\displaystyle (\operatorname {arccot} x)'={-1 \over 1+x^{2}}\,}](//wikimedia.org/api/rest_v1/media/math/render/svg/97dc76820f8146ce36f8bbd6f427d1989044402f) |
![{\displaystyle (\sinh x)'=\cosh x={\frac {e^{x}+e^{-x}}{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/cd0e3e8980164e7de16899715de99be8d68329b7) |
![{\displaystyle (\operatorname {arcsinh} \,x)'={1 \over {\sqrt {x^{2}+1}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3e2513a729a78510e03ba109c345c4cfe28e03bd) |
![{\displaystyle (\cosh x)'=\sinh x={\frac {e^{x}-e^{-x}}{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/d858f5de93aa418df24f6f953e85d1c95587ef7f) |
![{\displaystyle (\operatorname {arccosh} \,x)'={1 \over {\sqrt {x^{2}-1}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/fb5ae509faf501bd0910473f2d25bec2dc908c1a) |
![{\displaystyle (\tanh x)'=\operatorname {sech} ^{2}\,x}](//wikimedia.org/api/rest_v1/media/math/render/svg/bc0c134bf0eafdb91c3ad7b134a362efc450eb12) |
![{\displaystyle (\operatorname {arctanh} \,x)'={1 \over 1-x^{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/6473560357b3480aa329b9155f3e5cf1e869e3b1) |
![{\displaystyle (\operatorname {sech} \,x)'=-\tanh x\,\operatorname {sech} \,x}](//wikimedia.org/api/rest_v1/media/math/render/svg/abcfeea34ec248db2a3bbc9fc7afc3842a553fe5) |
![{\displaystyle (\operatorname {arcsech} \,x)'={-1 \over x{\sqrt {1-x^{2}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/3a87da394f1af5eaa34f57b9ec8bd5729721cc75) |
![{\displaystyle (\operatorname {csch} \,x)'=-\,\operatorname {coth} \,x\,\operatorname {csch} \,x}](//wikimedia.org/api/rest_v1/media/math/render/svg/8e57a9a8e61e37f893533f3b160cb2a67df8fea7) |
![{\displaystyle (\operatorname {arccsch} \,x)'={-1 \over |x|{\sqrt {1+x^{2}}}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/cd8776d8c87fbc875c2e41a44204ec49a0048d76) |
![{\displaystyle (\operatorname {coth} \,x)'=-\,\operatorname {csch} ^{2}\,x}](//wikimedia.org/api/rest_v1/media/math/render/svg/e18a260c8711eb1c0c05928ab6c6704e02ec9004) |
![{\displaystyle (\operatorname {arccoth} \,x)'={1 \over 1-x^{2}}}](//wikimedia.org/api/rest_v1/media/math/render/svg/a7f384ed50f7ec5fcfd48e901823f39a1baeacbb) |