\[(c)'=0 \]

\[(x^{\mu})'=ux^{\mu-1} \]

\[(\sin x)'=\cos x \]

\[(\cos x)'=-\sin x \]

\[(\tan x)'=\sec ^{2}x \]

\[(\cot x)'=-\csc ^{2}x \]

\[(\sec x)'=\sec x \tan x \]

\[(\csc x)'=-\csc x\cot x \]

\[(a^{x})'=a^{x}\ln a \]

\[(e^{x})'=e^{x} \]

\[(\log_{a}x)'=\frac{1}{x\ln a} \]

\[(\ln x)'=\frac{1}{x} \]

\[(\arcsin x)'=\frac{1}{\sqrt{1-x^{2}}} \]

\[(\arccos x)'=-\frac{1}{\sqrt{1-x^{2}}} \]

\[(\arctan x)'=\frac{1}{1+x^{2}} \]

\[(\text{arccot} x)'=-\frac{1}{1-x^{2}} \]

\[(u\pm v')=u' \pm v' \]

\[(uv)'=u'v+uv' \]

\[(\frac{u}{v})'=\frac{u'v-uv'}{v^{2}}, \frac{dy}{dx}=\frac{1}{\frac{dx}{dy}} \]