$$ \begin{aligned} c'&=0\\ (x^2)'&=ax^{a-1}\ , (a \in R)\\ (\log _ax)'&=\frac{1}{x\ln a}\ ,(a\gt 0,a\neq1)\\ (\ln x)'&=\frac{1}{x}\\ (a^x)'&=a^x\ln a\ ,(a\gt 0,a\neq1)\\ (e^x)'&=e^x\\ (\sin x)'&=\cos x\\ (\cos x)'&=-\sin x\\ (\tan x)'&=\sec ^2x\\ (\cot x)'&=-\csc ^2x\\ (\sec x)'&=\sec x\tan x\\ (\csc x)'&=-\sec x\cot x\\ (\arcsin x)'&=\frac{1}{\sqrt[]{1-x^2}}\\ (\arccos x)'&=-\frac{1}{\sqrt[]{1-x^2}}\\ (\arctan x)'&=\frac{1}{1+x^2}\\ (arccotx)'&=-\frac{1}{1+x^2} \end{aligned} $$

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