The set of points where the functions f given by $f(x)=|2x-1|\sin x$ is differentiable is

Question

$$\begin{array}{1 1}(A)\;R & (B)\;R-\left \{\frac{1}{2}\right \}\\(C)\;(0,\infty) & (D)\;none\;of\;these.\end{array}$$