So how can we rearrange this a little bit so that it could be defined for negative values as well? Well, one possibility is to think about the natural log of the absolute value of x. So I'll put a little question mark here because we don't really know what the derivative of this thing is going to be. And I'm not going to rigorously prove it here, but I will give you kind of the conceptual understanding. So to understand it, let's plot the natural log of x. And I had done this ahead of time. So that right over there is roughly what the graph of the natural log of x looks like.