$$\displaystyle\frac{d}{d x } \left( \frac{ \sqrt{ 1- \cos x } }{ \sqrt{ 2 } } \right)$$
$\frac{\sqrt{\frac{2}{-\cos(x)+1}}\sin(x)}{4}$
$\frac{\sqrt{2}\left(2\cos(x)\left(-\cos(x)+1\right)-\left(\sin(x)\right)^{2}\right)}{8\left(-\cos(x)+1\right)^{\frac{3}{2}}}$
