Tabelas de engenharia/Tabela de derivadas

Tabela de Deriivadas
$\frac{d}{dx}c=0$
$\frac{d}{dx}x=1$
$\frac{d}{dx}cx=c$
$\frac{d}{dx}|x|=\frac{x}{|x|}=\mathrm{sgn}x,x\ne 0$
$\frac{d}{dx}{x}^c=c{x}^{c-1}$ where both xc and cxc-1 are defined.
$\frac{d}{dx}\left(\frac{1}{x}\right)=\frac{d}{dx}\left(x^{-1}\right)=-x^{-2}=-\frac{1}{x^2}$
$\frac{d}{dx}\left(\frac{1}{x^c}\right)=\frac{d}{dx}\left(x^{-c}\right)=-\frac{c}{x^{c+1}}$
$\frac{d}{dx}\sqrt{x}=\frac{d}{dx}{x}^{\frac{1}{2}}=\frac{1}{2}{x}^{-\frac{1}{2}}=\frac{1}{2\sqrt{x}}$ x > 0
$\frac{d}{dx}{c}^x=c^x\ln c$ c > 0
$\frac{d}{dx}{e}^x=e^x$
$\frac{d}{dx}{\log }_{c}x=\frac{1}{x\ln c}$ c > 0, $c\ne 1$
$\frac{d}{dx}\ln x=\frac{1}{x}$
$\frac{d}{dx}\sin x=\cos x$
$\frac{d}{dx}\cos x=-\sin x$
$\frac{d}{dx}\tan x={\sec }^{2}x$
$\frac{d}{dx}\sec x=\tan x\sec x$
$\frac{d}{dx}\cot x=-{\csc }^{2}x$
$\frac{d}{dx}\csc x=-\csc x\cot x$
$\frac{d}{dx}\arcsin x=\frac{1}{\sqrt{1-x^2}}$
$\frac{d}{dx}\arccos x=\frac{-1}{\sqrt{1-x^2}}$
$\frac{d}{dx}\arctan x=\frac{1}{1+x^2}$
$\frac{d}{dx}\mathrm{arcsec}x=\frac{1}{|x|\sqrt{x^2-1}}$
$\frac{d}{dx}\mathrm{arccot}x=\frac{-1}{1+x^2}$
$\frac{d}{dx}\mathrm{arccsc}x=\frac{-1}{|x|\sqrt{x^2-1}}$
$\frac{d}{dx}\sinh x=\cosh x$
$\frac{d}{dx}\cosh x=\sinh x$
$\frac{d}{dx}\tanh x={\text{sech}}^{2}x$
$\frac{d}{dx}\text{sech}x=-\tanh x\text{sech}x$
$\frac{d}{dx}\text{coth}x=-{\text{csch}}^{2}x$
$\frac{d}{dx}\text{csch}x=-\text{coth}x\text{csch}x$
$\frac{d}{dx}\text{arcsinh}x=\frac{1}{\sqrt{x^2+1}}$
$\frac{d}{dx}\text{arccosh}x=\frac{1}{\sqrt{x^2-1}}$
$\frac{d}{dx}\text{arctanh}x=\frac{1}{1-x^2}$
$\frac{d}{dx}\text{arcsech}x=\frac{1}{x\sqrt{1-x^2}}$
$\frac{d}{dx}\text{arccoth}x=\frac{1}{1-x^2}$
$\frac{d}{dx}\text{arccsch}x=\frac{-1}{|x|\sqrt{1+x^2}}$