question_answer

If \[f(x)=\left| \begin{matrix}    \cos x & x & 1  \\    2\sin x & {{x}^{2}} & 2x  \\    \tan x & x & 1  \\ \end{matrix} \right|\] then \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\left[ \frac{f'(x)}{x} \right]\] is ________.

A)  \[-1\]                           

B)  \[1\]

C)  \[-2\]   

D)  \[2\]

E)  None of these