First, notice that we have two vertical asymptotes at x = 6 and x = −6. This means that the graph of the
derivative will also have vertical asymptotes at x = 6 and x = −6. Next, notice that the curve is always
decreasing. This means that the graph of the derivative will always be negative. Moving from left to right,
the graph starts out close to flat, so the derivative will be close to zero. Then, the graph gets very steep
and points downward, so the graph of the derivative will be negative and getting more negative. Then, we
have the asymptote x = −6. Next, the graph begins very steep and negative and starts to flatten out as we
approach the origin. At the origin, the slope of the graph is approximately − . This means that the graph
of the derivative will increase until it reaches (0, − ). Then, the graph starts to get steep again as we
approach the other asymptote x = 6. Thus, the graph will get more negative again. Finally, to the right of
the asymptote x = 6, the graph starts out steep and negative and flattens out, approaching zero. This means
that the graph of the derivative will start out very negative and will approach zero. If we now sketch the
derivative, it looks something like the following: