$$ g' = | \frac{\partial x_{\mu}}{\partial x_{\sigma'}} | |
\frac{\partial x_{\nu}}{\partial x_{\tau'}} | | g_{\mu \nu} | = |
\frac{\partial x_{\mu}}{\alpha_{\sigma'}} | g $$
or
(A)
$$ \sqrt{g'} = | \frac{\partial x_{\mu}}{\partial x_{\sigma'}} |
\sqrt{g} $$