Derivative of Real Area Hyperbolic Cosine

Theorem
Let $x \in \R_{>1}$ be a real number.

Let $\cosh^{-1} x$ be the inverse hyperbolic cosine of $x$.

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

Proof
The positive square root needs is taken because Inverse Hyperbolic Cosine is Strictly Increasing.