\[ \newcommand{\csch}{\mathop{\rm csch}\nolimits} \newcommand{\sech}{\mathop{\rm sech}\nolimits} \newcommand{\sgn}{\mathop{\rm sgn}\nolimits} \]

\[\frac{d}{dx}\exp x=\exp x\] \[\frac{d}{dx}\log|x|=\frac{1}{x}\] \[\frac{d}{dx}\sin x=\cos x\] \[\frac{d}{dx}\cos x=-\sin x\] \[\frac{d}{dx}\tan x=\sec^2x\] \[\frac{d}{dx}\cot x=-\csc^2x\] \[\frac{d}{dx}\sec x=\sec x\tan x\] \[\frac{d}{dx}\csc x=-\csc x\cot x\] \[\frac{d}{dx}\sin^{-1}x=\frac{1}{\sqrt{1-x^2}}\] \[\frac{d}{dx}\cos^{-1}x=\frac{-1}{\sqrt{1-x^2}}\] \[\frac{d}{dx}\tan^{-1}x=\frac{1}{1+x^2}\] \[\frac{d}{dx}\cot^{-1}x=\frac{-1}{1+x^2}\] \[\frac{d}{dx}\sec^{-1}x=\frac{1}{|x|\sqrt{x^2-1}}\] \[\frac{d}{dx}\csc^{-1}x=\frac{-1}{|x|\sqrt{x^2-1}}\] \[\frac{d}{dx}\sinh x=\cosh x\] \[\frac{d}{dx}\cosh x=\sinh x\] \[\frac{d}{dx}\tanh x=\sech^2x\] \[\frac{d}{dx}\coth x=-\csch^2x\] \[\frac{d}{dx}\sech x=-\sech x\tanh x\] \[\frac{d}{dx}\csch x=-\csch x\coth x\] \[\frac{d}{dx}\sinh^{-1}x=\frac{1}{\sqrt{x^2+1}}\] \[\frac{d}{dx}\cosh^{-1}|x|=\frac{\sgn x}{\sqrt{x^2-1}}\] \[\frac{d}{dx}\tanh^{-1}x=\frac{1}{1-x^2}\] \[\frac{d}{dx}\coth^{-1}x=\frac{1}{1-x^2}\] \[\frac{d}{dx}\sech^{-1}|x|=\frac{-1}{x\sqrt{1-x^2}}\] \[\frac{d}{dx}\csch^{-1}x=\frac{-1}{|x|\sqrt{1+x^2}}\]