Derivative of Hermite Spline

I’m playing around with object movement using hermite splines but I need to be able to break a spline in the middle so that the movement can be changed at any time, for that I need the derivative of the existing spline so I can create a new one from that point and keep the movement smooth.

So my question is: Is there an existing function that can calculate the derivative of a hermite spline?

Or will I have to a write my own?

There is nothing in MonoGame for that. You might find something in another library, or you might end up writing your own.