information:extraction
Derivatives

d d x sinh x = cosh x d d x cosh x = sinh x d d x tanh x = 1 − tanh 2 x = sech 2 x = 1 cosh 2 x d d x coth x = 1 − coth 2 x = − csch 2 x = − 1 sinh 2 x x ≠ 0 d d x sech x = − tanh x sech x d d x csch x = − coth x csch x x ≠ 0 {\displaystyle {\begin{aligned}{\frac {d}{dx}}\sinh x&=\cosh x\\{\frac {d}{dx}}\cosh x&=\sinh x\\{\frac {d}{dx}}\tanh x&=1-\tanh ^{2}x=\operatorname {sech} ^{2}x={\frac {1}{\cosh ^{2}x}}\\{\frac {d}{dx}}\coth x&=1-\coth ^{2}x=-\operatorname {csch} ^{2}x=-{\frac {1}{\sinh ^{2}x}}&&x\neq 0\\{\frac {d}{dx}}\operatorname {sech} x&=-\tanh x\operatorname {sech} x\\{\frac {d}{dx}}\operatorname {csch} x&=-\coth x\operatorname {csch} x&&x\neq 0\end{aligned}}} d d x arsinh x = 1 x 2 + 1 d d x arcosh x = 1 x 2 − 1 1 < x d d x artanh x = 1 1 − x 2 | x | < 1 d d x arcoth x = 1 1 − x 2 1 < | x | d d x arsech x = − 1 x 1 − x 2 0 < x < 1 d d x arcsch x = − 1 | x | 1 + x 2 x ≠ 0 {\displaystyle {\begin{aligned}{\frac {d}{dx}}\operatorname {arsinh} x&={\frac {1}{\sqrt {x^{2}+1}}}\\{\frac {d}{dx}}\operatorname {arcosh} x&={\frac {1}{\sqrt {x^{2}-1}}}&&1<x\\{\frac {d}{dx}}\operatorname {artanh} x&={\frac {1}{1-x^{2}}}&&|x|<1\\{\frac {d}{dx}}\operatorname {arcoth} x&={\frac {1}{1-x^{2}}}&&1<|x|\\{\frac {d}{dx}}\operatorname {arsech} x&=-{\frac {1}{x{\sqrt {1-x^{2}}}}}&&0<x<1\\{\frac {d}{dx}}\operatorname {arcsch} x&=-{\frac {1}{|x|{\sqrt {1+x^{2}}}}}&&x\neq 0\end{aligned}}}