Derivative of Legendre chi 2

Proposition: The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x} \chi_2(x) = \dfrac{\mathrm{arctanh}(x)}{x},$$ where $\chi$ denotes the Legendre chi function and $\mathrm{arctanh}$ denotes the inverse hyperbolic tangent function.

Proof: █