f′(x)=x(π−cos−1(sin∣x∣))=x(π(2π−sin−1(sin∣x∣))=x(2π+∣x∣)
f(x)={\begin{matrix}x(\frac{\pi }{2}+x) & x\geq 0 \\ x(\frac{\pi }{2}-x) & x<0\end{matrix}
{f}^{'}(x)={\begin{matrix}\frac{\pi }{2}+2x & x\geq 0 \\ \frac{\pi }{2}-2x & x<0\end{matrix}
f′(x) is increasing in (0,2π) and decreasing in (2−π,0).