Find the derivative of the piece-wise defined function. (Enter DNE if the function is not differentiable.)
$f(x) = \begin{cases} -x^2, & \text{if } x \le 0 \\ x^2, & \text{if } x > 0 \end{cases}$
$f'(x) = \begin{cases} \text{ }, & \text{if } x < 0 \\ \text{ }, & \text{if } x = 0 \\ \text{ }, & \text{if } x > 0 \end{cases}$