But the left side of the natural log of the absolute value of x is going to be its mirror image if you were to reflect around the y-axis. It's going to look something like this. So what's nice about this function is you see it's defined everywhere except for, I'm trying to draw it as symmetrically as possible, it's defined everywhere except for x equals 0. So if you combine this pink part and this part on the right, if you combine both of these, you get y is equal to the natural log of the absolute value of x. Now let's think about its derivative. We already know what the derivative of the natural log of x is. And for positive values of x, let me write this down.