# តារាងដេរីវេធម្មតា

ខាងក្រោមនេះគឺជាតារាងនៃអនុគមន៍ដេរីវេដែលត្រូវគេប្រើជារឿយៗ។

ដែននៃ${\displaystyle D_{f}\,\!}$ អនុគមន៍${\displaystyle f(x)\,\!}$ ដែននៃដេរីវេ${\displaystyle D_{f'}\,\!}$ ដេរីវេ${\displaystyle f'(x)\,\!}$ លក្ខខណ្ឌ
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle k\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle 0\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle x\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle 1\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle x^{2}\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle 2x\,\!}$
${\displaystyle \mathbb {R} _{+}\,\!}$ ${\displaystyle {\sqrt {x}}\,\!}$ ${\displaystyle \mathbb {R} _{+}^{*}\,\!}$ ${\displaystyle {\frac {1}{2{\sqrt {x}}}}\,\!}$
${\displaystyle \mathbb {R} ^{*}\,\!}$ ${\displaystyle {\frac {1}{x}}\,\!}$ ${\displaystyle \mathbb {R} ^{*}\,\!}$ ${\displaystyle -{\frac {1}{x^{2}}}\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle x^{n}\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle nx^{n-1}\,\!}$ ${\displaystyle n\in \mathbb {N} \,\!}$
${\displaystyle \mathbb {R} ^{*}\,\!}$ ${\displaystyle {\frac {1}{x^{n}}}\,\!}$ ${\displaystyle \mathbb {R} ^{*}\,\!}$ ${\displaystyle -{\frac {n}{x^{n+1}}}\,\!}$ ${\displaystyle n\in \mathbb {N} \,\!}$
${\displaystyle \mathbb {R} _{+}\,\!}$ ${\displaystyle {\sqrt[{n}]{x}}\,\!}$ ${\displaystyle \mathbb {R} _{+}^{*}\,\!}$ ${\displaystyle {\frac {1}{n{\sqrt[{n}]{x^{n-1}}}}}\,\!}$ ${\displaystyle n\in \mathbb {N} ~}$
${\displaystyle \mathbb {R} _{+}\,\!}$ ${\displaystyle x^{\alpha }\,\!}$ ${\displaystyle \mathbb {R} _{+}\,\!}$ ${\displaystyle \alpha x^{\alpha -1}\,\!}$ ${\displaystyle \alpha \geq 1\,\!}$
${\displaystyle \mathbb {R} _{+}\,\!}$ ${\displaystyle x^{\alpha }\,\!}$ ${\displaystyle \mathbb {R} _{+}^{*}\,\!}$ ${\displaystyle \alpha x^{\alpha -1}\,\!}$ ${\displaystyle 0<\alpha <1\,\!}$
${\displaystyle \mathbb {R} _{+}^{*}\,\!}$ ${\displaystyle x^{\alpha }\,\!}$ ${\displaystyle \mathbb {R} _{+}^{*}\,\!}$ ${\displaystyle \alpha x^{\alpha -1}\,\!}$ ${\displaystyle \alpha <0\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle \sin x\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle \cos x\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle \cos x\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle -\sin x\,\!}$
${\displaystyle \mathbb {R} \backslash \left({\frac {\pi }{2}}+\pi \mathbb {Z} \right)\,\!}$ ${\displaystyle \tan x\,\!}$ ${\displaystyle \mathbb {R} \backslash \left({\frac {\pi }{2}}+\pi \mathbb {Z} \right)\,\!}$ ${\displaystyle {\frac {1}{\cos ^{2}x}}=1+\tan ^{2}x\,\!}$
${\displaystyle \mathbb {R} \backslash \left(\pi \mathbb {Z} \right)\,\!}$ ${\displaystyle \cot x\,\!}$ ${\displaystyle \mathbb {R} \backslash \left(\pi \mathbb {Z} \right)\,\!}$ ${\displaystyle -{\frac {1}{\sin ^{2}x}}=-1-\cot ^{2}x\,\!}$
${\displaystyle [-1,1]\,\!}$ ${\displaystyle \arcsin x\,\!}$ ${\displaystyle ]-1,1[\,\!}$ ${\displaystyle {\frac {1}{\sqrt {1-x^{2}}}}\,\!}$
${\displaystyle [-1,1]\,\!}$ ${\displaystyle \arccos x\,\!}$ ${\displaystyle ]-1,1[\,\!}$ ${\displaystyle -{\frac {1}{\sqrt {1-x^{2}}}}\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle \arctan x\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle {\frac {1}{1+x^{2}}}\,\!}$
${\displaystyle \mathbb {R} _{+}^{*}\,\!}$ ${\displaystyle \ln x\,\!}$ ${\displaystyle \mathbb {R} _{+}^{*}\,\!}$ ${\displaystyle {\frac {1}{x}}\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle e^{x}\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle e^{x}\,\!}$
${\displaystyle \mathbb {R} _{+}^{*}\,\!}$ ${\displaystyle \log _{a}x\,\!}$ ${\displaystyle \mathbb {R} _{+}^{*}\,\!}$ ${\displaystyle {\frac {1}{x\ln a}}\,\!}$ ${\displaystyle a>0\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle a^{x}\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle a^{x}\ln a\,\!}$ ${\displaystyle a>0\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle \operatorname {sh} x\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle \operatorname {ch} x\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle \operatorname {ch} x\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle \operatorname {sh} x\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle \operatorname {th} x\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle {\frac {1}{\operatorname {ch} ^{2}x}}\,\!}$
${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle \ \operatorname {argsh} \,x\,\!}$ ${\displaystyle \mathbb {R} \,\!}$ ${\displaystyle {\frac {1}{\sqrt {1+x^{2}}}}\,\!}$
${\displaystyle ]1,+\infty [\,\!}$ ${\displaystyle \ \operatorname {argch} \,x\,\!}$ ${\displaystyle ]1,+\infty [\,\!}$ ${\displaystyle {\frac {1}{\sqrt {x^{2}-1}}}\,\!}$
${\displaystyle ]-1,1[\,\!}$ ${\displaystyle \ \operatorname {argth} \,x\,\!}$ ${\displaystyle ]-1,1[\,\!}$ ${\displaystyle {\frac {1}{1-x^{2}}}\,\!}$