Derivative-1

三角函数

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

反三角函数

\frac{\mathrm{d}}{\mathrm{d}x}\arcsin x=\frac{1}{\sqrt{ 1-x^2 }}
\frac{\mathrm{d}}{\mathrm{d}x}\arccos x=-\frac{1}{\sqrt{ 1-x^2 }}
\frac{\mathrm{d}}{\mathrm{d}x}\arctan x=\frac{1}{1+x^2}
\frac{\mathrm{d}}{\mathrm{d}x}\text{arccot}x=-\frac{1}{1+x^2}
\frac{\mathrm{d}}{\mathrm{d}x}\text{{arcsec}} x=\frac{1}{\lvert x\rvert \sqrt{ x^{2}-1 }}
\frac{\mathrm{d}}{\mathrm{d}x}\text{arccsc}x=-\frac{1}{\lvert x\rvert \sqrt{ x^2 -1}}