Let f(x)=x cos^-1(- sin |x|), x ∈[-(π)/2, (π)/2], then which of the following is true?

$\displaystyle f$ is not differentiable at $\displaystyle x=0$

$\displaystyle f^{\prime}(0)=-\frac{\pi}{2}$

$\displaystyle f^{\prime}$ is decreasing in $\displaystyle \left(-\frac{\pi}{2}, 0\right)$ and increasing in $\displaystyle \left(0, \frac{\pi}{2}\right)$

$\displaystyle f^{\prime}$ is increasing in $\displaystyle \left(-\frac{\pi}{2}, 0\right)$ and decreasing in $\displaystyle \left(0, \frac{\pi}{2}\right)$