[tex] \left( {\sin x} \right)^\prime = \cos x \hfill \\ \left( {\cos x} \right)^\prime = - \sin x \hfill \\ \left( {\tan x} \right)^\prime = \sec ^2 x \hfill \\ \left( {\cot x} \right)^\prime = - \csc ^2 x \hfill \\ \left( {\sec x} \right)^\prime = \sec x\tan x \hfill \\ \left( {\csc x} \right)^\prime = - \csc x\cot x \hfill \\[/tex]
[tex] \left( {\arcsin x} \right)^\prime = \dfrac{1} {{\sqrt {1 - x^2 } }} \hfill \\ \left( {\arccos x} \right)^\prime = - \dfrac{1} {{\sqrt {1 - x^2 } }} \hfill \\ \left( {\arctan x} \right)^\prime = \dfrac{1} {{1 + x^2 }} \hfill \\[/tex]
[tex] \left( {arc\cot x} \right)^\prime = - \dfrac{1} {{1 + x^2 }} \hfill \\ \left( {arc\sec x} \right)^\prime = \dfrac{1} {{\left| x \right|\sqrt {x^2 - 1} }} \hfill \\ \left( {arc\csc x} \right)^\prime = - \dfrac{1} {{\left| x \right|\sqrt {x^2 - 1} }} \hfill \\[/tex]
