Solve this following
Question:

Let $f(x)=x \cos ^{-1}(-\sin |x|), x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$, then

which of the following is true ?

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

2. $f$ is not differentiable at $x=0$

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

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

Correct Option: 1

Solution: