question_answer

If \[f\,\,(x)=\left\{ \begin{matrix}    x\frac{{{e}^{(1/x)}}-{{e}^{(-1/x)}}}{{{e}^{(1/x)}}+{{e}^{(-1/x)}}},\,\,\,\,\,\,\,x\ne 0  \\    0,\,\,\,\,\,\,x=0  \\ \end{matrix} \right.,\] then which of the following in true

A)  f is continuous and differentiable at every point

B)  f is continuous at every point but is not differentiable

C)  f is differentiable at every point

D)  f is differentiable only at the origin

E)  None of these