Math Formulas || Limits and Derivaties || Inverse Hyperbolic Derivatives

$\dfrac{d}{dx}~ (\sinh^{-1} u) = \dfrac{1}{\sqrt{1+u^2}}\dfrac{du}{dx} $
$\dfrac{d}{dx}~ (\cosh^{-1} u) $ $= \dfrac{1}{\sqrt{u^2-1}}\dfrac{du}{dx}~, u > 1 $
$\dfrac{d}{dx}~ (\tanh^{-1} u) $ $= \dfrac{1}{1-u^2}\dfrac{du}{dx}~, \left|u\right| < 1 $
$\dfrac{d}{dx}~ (\coth^{-1} u) $ $= \dfrac{1}{1-u^2}\dfrac{du}{dx}~, \left|u\right| > 1 $
$\dfrac{d}{dx}~ (\text{sech}^{-1}~u) $ $= -~\dfrac{1}{u\sqrt{1-u^{2}}}\dfrac{du}{dx}~, 0 < u < 1 $
$\dfrac{d}{dx}~ (\text{csch}^{-1}~u) $ $= -~\dfrac{1}{\left|u\right|\sqrt{1+u^{2}}}\dfrac{du}{dx}~, u \neq 0 $