\begin{matrix} {d \over dx} \sin x =& \cos x         ,& {d \over dx} \arcsin x =&{1 \over \sqrt{1 - x^2}     } \  \ {d \over dx} \cos x =& -\sin x        ,& {d \over dx} \arccos x =&{-1 \over \sqrt{1 - x^2}}      \  \ {d \over dx} \tan x =& \sec^2 x       ,& {d \over dx} \arctan x =&{ 1 \over 1 + x^2}            \  \ {d \over dx} \cot x =& -\csc^2 x      ,& {d \over dx} \arccot x =&-{1 \over 1 + x^2}             \  \ {d \over dx} \sec x =& \tan x \sec x  ,& {d \over dx} \arcsec x =&{ 1 \over |x|\sqrt{x^2 - 1}}   \  \ {d \over dx} \csc x =& -\csc x \cot x ,& {d \over dx} \arccsc x =&-{1 \over |x|\sqrt{x^2 - 1}} \end{matrix}