differentiate $y = (\sin x)^x + \sin^{-1} \sqrt x$

Question

$(A) \frac{dy}{dx} = (\sin x)^x [ x \cot x + log \; \sin x ] -\frac{1}{2 {x(1-x)}}$
$(B) \frac{dy}{dx} = (\sin x)^x [ x \cot x + log \; \sin x ] -\frac{1}{2 \sqrt{x(1-x)}}$
$(C) \frac{dy}{dx} = (\sin x)^x [ x \cot x + log \; \sin x ] +\frac{1}{2 \sqrt{x(1-x)}}$
$(D) \frac{dy}{dx} = (\sin x)^x [ x \cot x + log \; \sin x ] +\frac{1}{2 {x(1-x)}}$