Derivative of Inverse Hyperbolic Cotangent

Theorem
Let $S$ denote the union of the unbounded open real intervals:
 * $S := \left({-\infty \,.\,.\, -1}\right) \cup \left({1 \,.\,.\, +\infty}\right)$

Let $x \in S$.

Let $\coth^{-1} x$ be the inverse hyperbolic cotangent of $x$.

Then:
 * $\dfrac {\mathrm d}{\mathrm d x} \left({\coth^{-1} x}\right) = \dfrac {-1} {x^2 - 1}$

Also defined as
This result can also be (and usually is) reported as:
 * $\dfrac {\mathrm d}{\mathrm d x} \left({\coth^{-1} x}\right) = \dfrac 1 {1 - x^2}$

but this obscures the fact that $x^2 > 1$ in order for it to be defined.