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Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be the function defined by $f\left ( x \right )=\frac{\sin \: x}{\left | x \right |+\cos \: x}$. Then 

  1. $f$ is differentiable at all $x\in\mathbb{R}$
  2. $f$ is not differentiable at $x=0$
  3. $f$ is differentiable at $x=0$ but ${f}'$ is not continuous at $x=0$
  4. $f$ is not differentiable at $x=\frac{\pi }{2}.$
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