导数基本公式

Guderian出品

$(1)(C)’ = 0$

$(2)(x^a)’=ax^{a-1}$

$(3)(a^x)’=a^x\ln a (a>0且a\not=1)$

$(4)(e^x)’=e^x$

$(5)(\log_ax)’=\frac{1}{x\ln a}(a>0且a\not=1)$

$(6)(\ln x)’=\frac1{x}$

$(7)(\sin x)’=\cos x$

$(8)(\cos x)’=-\sin x$

$(9)(\tan x)’=\frac1{\cos^2x}=\sec^2x$

$(10)(\cot x)’=\frac1{-\sin^2 x}=-\csc^2x$

$(11)(\sec x)’=\sec x\tan x$

$(12)(\csc x)’=-\csc x\cot x$

$(13)(\arcsin x)’=\frac1{\sqrt{1-x^2}}$

$(14)(\arccos x)’=-\frac1{\sqrt{1-x^2}}$

$(15)(\arctan x)’=\frac1{1+x^2}$

$(16)(\mathrm{arccot} x)’=-\frac1{1+x^2}$