Mathematics - Continuity - Differentiability Question with Solution | TestHub

$$f(x)=\{\begin{array}{ll}\frac{x}{1-x},& x<0\\ \frac{x}{1+x},& x\ge 0\end{array}\Rightarrow f^{\prime }(x)=\{\begin{array}{ll}\frac{1}{(1-x{)}^2},& x<0\\ \frac{1}{(1+x{)}^2},& x\ge 0\end{array}$$ $\therefore f^{\prime }(x)$ exist at everywhere.