Differentiate w.r.t. x the function $cot^{-1} \begin{bmatrix} \frac{{\sqrt {1+sin \: x}} + {\sqrt{1-sin \: x}}} {{\sqrt {1+sin \: x}} - {\sqrt{1-sin \: x}}} \\[0.3em] \end{bmatrix}$, where $0 < x < \frac{\pi}{2}$

Question

$\begin{array}{1 1} \frac{3x}{2} \\ \frac{x}{2} \\ \frac{1}{2} \\ \frac{-x}{2} \end{array}$