标签： 高等数学基础

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

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

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

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

$(\ln x)’$ $=$ $\frac{1}{x}$

$(\log_{a}^{x})’$ $=$ $\frac{1}{x \ln a}$

$(e^{x})’$ $=$ $e^{x}$

$(a^{x})’$ $=$ $a^{x} \ln a$

$(\csc x)’$ $=$ $(\frac{1}{\sin x})’$ $=$ $- \csc x \cdot \cot x$

$(\sec x)’$ $=$ $(\frac{1}{\cos})’$ $=$ $\sec x \cdot \tan x$

$(\cot x)’$ $=$ $- \csc^{2} x$ $=$ $-(\frac{1}{\sin x})^{2}$

$(\tan x)’$ $=$ $\sec^{2} x$ $=$ $(\frac{1}{\cos x})^{2}$

$(\cos x)’$ $=$ $- \sin x$

$(\sin x)’$ $=$ $\cos x$

$(x^{\alpha})’$ $=$ $\alpha x^{\alpha – 1}$