For the function f(x)= e^sin |x|-|x|, x ∈ R, consider the following statements: Statement I: f is differentiable for all x ∈ R. Statement II: f is…

For the function $\displaystyle f(x)=\mathrm{e}^{\sin |x|}-|x|, x \in \mathbf{R}$, consider the following statements : Statement I : $\displaystyle f$ is differentiable for all $\displaystyle x \in \mathbf{R}$. Statement II : $\displaystyle f$ is increasing in $\displaystyle \left(-\pi,-\frac{\pi}{2}\right)$. In the light of the above statements, choose the correct answer from the options given below :