if $g$ be a continuous function not differentiable at $0$ Let $g$ be a continuous function not differentiable at $0$ with $g(0)=8$. Let $f(x)=x\,g(x)$ .Find $f'(0)$  
a)$0$
b)$4$
c)$2$
d)$8$   
I am getting that $f'(x)=g(x)+x\,g'(x)$. But since $g'(x)$ doesn't exist for $x=0$, hence $f'(x)=8$. Please help whether it is right or wrong

$\lim_{x \rightarrow 0} \dfrac{f(x)-f(0)}{x} =$
$\lim_{x \rightarrow 0} g(x) = g(0)$, since 
$g$ is continous at $0$.
Note: $g'(0)$ does not exist .
Which  answer?
