Out teacher never went over finding the derivative of absolute value functions, and I'm not sure how I will go about doing it. Should I make into a piece-wise function?
EDIT: We haven't done chain rule or power rule etc. We only know the definition of a limit $f(x+h)-f(x)\over h$
Hint: On the intervals $(-\infty, -1)$ and $(1,\infty)$, the function $|x^2-1|=x^2-1$. On the interval $(-1,1)$, the function $|x^2-1|=-(x^2-1)=1-x^2$. So you'll literally have different derivatives depending on the interval you're looking at.
Notice that the point $(-1,0)$ and $(0,1)$ isn't included. Can you tell why?