What is Derivative of order more than one? So, Its easy to geometrically interpret the first order derivative in a graph by drawing a tangent to the curve of any function showing derivative as same the slope of the line but how can we draw a second order derivative on the same graph or how can we visualise this derivative of a derivative & the story get more complicated for more higher order derivatives? 
 A: The second derivative of a function at a point will tell you about how the slope of the tangent line tends to change in a neighborhood of that point.
If the slope of the tangent line increases, then the graph of the function is convex in a neighborhood of that point. If the slope of the tangent line decreases, then the graph of the function is concave.
You can interpret the third derivative as how the convexity of the function changes.. This isn't very meaningful, but it helps you geometrically interpret at what points the third derivative becomes zero.
Beyond the third derivative, there's no geometric interpretation. But you can still think of the $n$-th derivative as the rate of change of the $(n-1)$-th derivative.
A: It's simply the derivative of the derivative of a function. So in the real world the second derivative would give you acceleration. A function that describes the position (p) at some time (t) of some object would have a first derivative that gives you the velocity and the second derivative would tell you the instantaneous rate of change of the velocity, or the acceleration.  
