Use the definition of a derivative to find $f'(0)$ where:

$$f(x) = \begin{cases} x^2 \sin \left(\frac{1}{x} \right) & x \neq 0 \\ 0 & x = 0\\ \end{cases}$$
If the derivative does not exist enter DNE.

$f'(0) =$
(you will lose 25% of your points if you do)