The set of all points where the function $f(x)=\large\frac{x}{(1+|x|)}$ is differentiable is

Question

$\begin{array}{1 1}(a)\;[-\infty,\infty]&(b)\;[0,\infty]\\(c)\;[-\infty,0]\cup [0,\infty]&(d)\;[0,\infty]\end{array}$