# Table of Derivatives

Keywords: table of derivatives, derivatives
$\frac{d}{dx}\left({x}^{n}\right)=n{x}^{n-1},n\ne 0$
$\frac{d}{dx}\left({a}^{x}\right)={a}^{x}lna$
$\frac{d}{dx}\left({e}^{x}\right)={e}^{x}$
$\frac{d}{dx}\left(lo{g}_{a}x\right)=\frac{1}{ln\phantom{\rule{thinmathspace}{0ex}}a}·\frac{1}{x}$
$\frac{d}{dx}\left(ln\phantom{\rule{thinmathspace}{0ex}}x\right)=\frac{1}{x}$
$\frac{d}{dx}\left(sin\phantom{\rule{thinmathspace}{0ex}}x\right)=cos\phantom{\rule{thinmathspace}{0ex}}x$
$\frac{d}{dx}\left(cos\phantom{\rule{thinmathspace}{0ex}}x\right)=-sin\phantom{\rule{thinmathspace}{0ex}}x$
$\frac{d}{dx}\left(tg\phantom{\rule{thinmathspace}{0ex}}x\right)=\frac{1}{co{s}^{2}\phantom{\rule{thinmathspace}{0ex}}x}$
$\frac{d}{dx}\left(ctg\phantom{\rule{thinmathspace}{0ex}}x\right)=-\frac{1}{si{n}^{2}\phantom{\rule{thinmathspace}{0ex}}x}$
$\frac{d}{dx}\left(arcsin\phantom{\rule{thinmathspace}{0ex}}x\right)=\frac{1}{\sqrt{1-{x}^{2}}}$
$\frac{d}{dx}\left(arccos\phantom{\rule{thinmathspace}{0ex}}x\right)=-\frac{1}{\sqrt{1-{x}^{2}}}$
$\frac{d}{dx}\left(arctg\phantom{\rule{thinmathspace}{0ex}}x\right)=\frac{1}{1+{x}^{2}}$
$\frac{d}{dx}\left(arcctg\phantom{\rule{thinmathspace}{0ex}}x\right)=-\frac{1}{1+{x}^{2}}$
$\frac{d}{dx}\left(sh\phantom{\rule{thinmathspace}{0ex}}x\right)=ch\phantom{\rule{thinmathspace}{0ex}}x$
$\frac{d}{dx}\left(ch\phantom{\rule{thinmathspace}{0ex}}x\right)=sh\phantom{\rule{thinmathspace}{0ex}}x$
$\frac{d}{dx}\left(th\phantom{\rule{thinmathspace}{0ex}}x\right)=\frac{1}{c{h}^{2}\phantom{\rule{thinmathspace}{0ex}}x}$
$\frac{d}{dx}\left(cth\phantom{\rule{thinmathspace}{0ex}}x\right)=-\frac{1}{s{h}^{2}\phantom{\rule{thinmathspace}{0ex}}x}$
$\frac{d}{dx}\left(arsh\phantom{\rule{thinmathspace}{0ex}}x\right)=\frac{1}{\sqrt{1+{x}^{2}}}$
$\frac{d}{dx}\left(arch\phantom{\rule{thinmathspace}{0ex}}x\right)=\frac{1}{\sqrt{{x}^{2}-1}}$