question_answer

The domain of the derivative of the function \[f(x)=\left\{ \begin{matrix}    {{\tan }^{-1}}x, & if\,\,x||\,\le \,1  \\    \frac{1}{2}(|x|-1), & if\,\,|x|\,\le \,1  \\ \end{matrix} \right.\] is

A)  \[R-\left\{ 0 \right\}\]                  

B)  \[R-\left\{ 1 \right\}\]

C)  \[R-\left\{ -\,1 \right\}\]               

D)  \[R-\left\{ -\,1,1 \right\}\]

E)  None of these