តារាងដេរីវេធម្មតា

ខាងក្រោមនេះគឺជាតារាងនៃអនុគមន៍ដេរីវេដែលត្រូវគេប្រើជារឿយៗ។

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