Source: Thomas Moore, A General Relativity Workbook page 353.
I'm quite lost verifying the following:
$$\delta^{\beta}_\alpha - \frac{\partial x^\mu}{\partial x^{\prime\alpha}}\frac{\partial \xi^\beta}{\partial x^\mu} = \delta^\beta_\alpha - (\delta^\mu_\alpha-\partial^\prime _\alpha \xi^\mu)\partial_\mu \xi^\beta $$
I am aware that $$\frac{\partial x^\alpha}{\partial x^\beta}=\delta^\alpha_\beta$$ but I'm not sure at all where that other term is coming from.