Let $$f(x) = \begin{cases} -\left(4x+2\right) & \textrm{if }x < -1 \\ 2x^{2} & \textrm{if }-1 \leq x \leq 1 \\ 2x & \textrm{if }x > 1 \end{cases}$$
Find a formula for $f'(x)$.

Note: $f(x)$ is differentiable at $x=-1$, but is NOT differentiable at $x=1$. Can you see why that is so?

                $\text{if} \quad x<-1$
$f'(x)=$ $\text{if} \quad -1 \leq x <1$
                $\text{if} \quad x>1$