Thread: Derivative of a derivative question...

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?

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?

Originally Posted by Nervous

I'm betting the derivative of the derivative is the tangent line of the graph of the original derivative, yes?

Yes, it would be the slope of the tangent line to the first derivative's graph. We call this derivative the second derivative, usually denoted or . Similarly, we can find a third derivative by differentiating the second, and so on for higher orders.