导数的基本公式

$C\prime=0$ (c为任意常数)

$(x^\alpha)\prime=\alpha x^{\alpha-1}$

$a^x=a^x \ln{a}$

$(e^x)\prime=e^x$

$(\log_ax)\prime=\frac{1}{x \ln a}$

$(\ln x)\prime=\frac{1}{x}$

$(\sin x)\prime=\cos x$

$(\cos x)\prime=-\sin x$

$(\tan x)\prime=\sec^2 x$

$(\cot x)\prime=-\csc^2 x$

$(\sec x)\prime=\sec x\tan x$

$(\csc x)\prime=-\csc x\cot x$

$(\arcsin x)\prime=\frac{1}{\sqrt{1-x^2}}$

$(\arccos x)\prime=\frac{-1}{\sqrt{1-x^2}}$

$(\arctan x)\prime=\frac{1}{1+x^2}$

$(arccot x)\prime=\frac{-1}{1+x^2}$

导数的四则运算

$\bigg(u(x)+v(x)\bigg)\prime=u\prime(x)+v\prime(x)$

$\bigg(u(x)-v(x)\bigg)\prime=u\prime(x)-v\prime(x)$

$\bigg(u(x)v(x)\bigg)\prime=u(x)v\prime(x)+u\prime(x)v(x)$

$\bigg(\frac{v(x)}{u(x)}\bigg)\prime=\frac{u(x)v\prime(x)-u\prime(x)v(x)}{[u(x)]^2}$