# Derivatives and integrals of curves

Right off the bat, I’d like to emphasize that I’m not interested in the time derivative of functions, which I know can be accomplished under the Convert menu.

I’m interested in producing some plots of displacement, velocity, and acceleration. What I would like to do is draw a Bezier curve representing displacement, then have Synfig automatically take the derivative of this curve to plot the velocity, and then take one more derivative for the acceleration. I’m also interested in the reverse process-- graphing acceleration and using this plot to produce two antiderivatives to obtain displacement. Can this be done? I suppose I could do it with two Duplicate layers and a spline with hundreds of vertices, but suffice it to say that seems inelegant. I’ve also toyed around with the mathematics of Bezier curves but given up on it for now. Any thoughts?

By the way, you may want to check out this thread in which caryoscelus and I explain how to define a mathematical function from a graph. I would not be surprised if the solution here is related to that procedure.