Solve this following
Question:

If $f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x x^{2} & 2 x \\ \tan x & x & 1\end{array}\right|$, then $\lim _{x \rightarrow 0} \frac{f^{\prime}(x)}{x}$

1. exists and is equal to 0

2. exists and is equal to $-2$

3. exists and is equal to 2

4. does not exist

Correct Option: , 2

Solution: