Case 1:

$\displaystyle \nabla F(\mathbf{x}' ; \mathbf{x})$	$\displaystyle =$	$\displaystyle \nabla \frac{1}{4\pi} \mathrm{atan}\left(\frac{x'y'}{z'r'}\right)$	(39)
	$\displaystyle =$	$\displaystyle \frac{1}{4\pi} \left[ \frac{y'z'}{x'^2 + z'^2} \; , \; \frac{x'z'... ...2 + z'^2} \; , \; \frac{-x'y'(r'^2 + z'^2)}{(x'^2 + z'^2)(y'^2 + z'^2)} \right]$	(40)