Derivative-1

三角函数

\frac{d}{dx}\sin x=\cos x
\frac{d}{dx}\cos x=-\sin x
\frac{d}{dx}\tan x=\sec^2x
\frac{d}{dx}\cot x=-\csc^2x
\frac{d}{dx}\sec x=\sec x\tan x
\frac{d}{dx}\csc x=-\csc x\cot x

反三角函数

\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}\text{arccot}x=-\frac{1}{1+x^2}
\frac{d}{dx}\text{{arcsec}} x=\frac{1}{|x|\sqrt{ x^{2}-1 }}
\frac{d}{dx}\text{arccsc}x=-\frac{1}{|x|\sqrt{ x^2 -1}}