Actually, now that I asked, my scumbag brain gave me a good idea. I'm betting the derivative of the derivative is the tangent line of the graph of the original derivative, yes?
This isn't homework or even a problem I'm having, I'm just curious about something... When I first found out about derivatives, the book I was reading explained that the derivative is the slope of a curve that was infinitely zoomed in on. This would be the same thing as if you made a line that touched the curve in exactly one spot. However, what is the derivative of a derivative? Is it just infinitely zoomed in on an already infinitely zoomed in spot? I fail to imagine how another tangent line could touch the first tangent line in one spot, without crossing over it like an "x". Can anyone explain this to me?