Suppose that $f(x)$ is a differentiable function such that $f^{\prime}(x)$ is continuous, $f^{\prime}(0)=1$ and $f^{\prime \prime}(0)$ does not exist. Let $g(x)=x f^{\prime}(x)$. Then,
- A$g^{\prime}(0)$ does not exist
- B$g^{\prime}(0)=0$
- C$g^{\prime}(0)=1$
- D$g^{\prime}(0)=2$
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