基本初等函数导数公式表

( C ) ′ = 0 ,   C 为 常 数 \LARGE(C)'=0,\ C为常数 (C)′=0, C为常数

( n x ) ′ = n x ln ⁡ n \LARGE(n^x)'=n^x\ln n (nx)′=nxlnn ( e x ) ′ = e x \LARGE(e^x)'=e^x (ex)′=ex

( log ⁡ a x ) ′ = 1 x ln ⁡ a \LARGE(\log_ax)'=\frac1{x\ln a} (loga​x)′=xlna1​ ( ln ⁡ x ) ′ = 1 x \LARGE(\ln x)'=\frac1x (lnx)′=x1​

( x n ) ′ = n x n − 1 ,   n 为 任 意 实 数 \LARGE(x^n)'=nx^{n-1},\ n为任意实数 (xn)′=nxn−1, n为任意实数

( sin ⁡ x ) ′ = cos ⁡ x \LARGE(\sin x)'=\cos x (sinx)′=cosx ( cos ⁡ x ) ′ = − sin ⁡ x \LARGE(\cos x)'=-\sin x (cosx)′=−sinx ( tan ⁡ x ) ′ = sec ⁡ 2 x \LARGE(\tan x)^{\prime}=\sec ^{2} x (tanx)′=sec2x ( cot ⁡ x ) ′ = − csc ⁡ 2 x \LARGE(\cot x)^{\prime}=-\csc ^{2} x (cotx)′=−csc2x ( sec ⁡ x ) ′ = sec ⁡ x tan ⁡ x \LARGE(\sec x)^{\prime}=\sec x \tan x (secx)′=secxtanx ( csc ⁡ x ) ′ = − csc ⁡ x cot ⁡ x \LARGE(\csc x)^{\prime}=-\csc x \cot x (cscx)′=−cscxcotx

( arcsin ⁡ x ) ′ = 1 1 − x 2 \LARGE (\arcsin x)^{\prime}=\frac{1}{\sqrt{1-x^{2}}} (arcsinx)′=1−x2 ​1​ ( arccos ⁡ x ) ′ = − 1 1 − x 2 \LARGE (\arccos x)^{\prime}=-\frac{1}{\sqrt{1-x^{2}}} (arccosx)′=−1−x2 ​1​ ( arctan ⁡ x ) ′ = 1 1 + x 2 \LARGE (\arctan x)^{\prime}=\frac{1}{1+x^{2}} (arctanx)′=1+x21​ ( arccot ⁡ x ) ′ = − 1 1 + x 2 \LARGE (\operatorname{arccot} x)^{\prime}=-\frac{1}{1+x^{2}} (arccotx)′=−1+x21​