Derivative of Inverse Hyperbolic Tangent

Theorem
Let $S$ denote the open real interval:
 * $S := \left({-1 \,.\,.\, 1}\right)$

Let $x \in S$.

Let $\tanh^{-1} x$ be the inverse hyperbolic tangent of $x$.

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