Derivative of Inverse Hyperbolic Cosecant

Theorem
Let $x \in \R_{\ne 0}$.

Let $\operatorname{csch}^{-1} x$ be the inverse hyperbolic cosecant of $x$.

Then:
 * $\dfrac {\mathrm d}{\mathrm d x} \left({\operatorname{csch}^{-1} x}\right) = \dfrac {-1} {\left\vert{x}\right\vert \sqrt{1 + x^2} }$