Let

$f(x)=\{\begin{array}{ccc}{x}^{4}sin(\frac{1}{x})& if& x0\\ 0& if& x=0\end{array}$

$($i$)$ Find $f^{\text{'}}(x)$ for all xinR.

$($ii$)$ Determine whether $f^{\text{'}}$ is continuous at $x=0$ and justify your answer.