I can understand the , what's messing me up is the . What is this?

I'll ignore the last half of this and just focus on the absolute value part.

We need to find out where .

So x = 0 or

Thus the solutions are .

Now we ask, where is negative? We have 4 test intervals:

:

:

:

:

All of this leads to the following:

Now you can take your derivative on the "piece-wise defined" function, like you would any other function.

-Dan