Get the derivative of a path

[Mearleo]

I want to get the derivative of any arbitrary path at a certain sample point (needed for my use case). My approach is to draw a small circle at the sample point, get the intersection with the path and then calculate the difference of the intersection and the sample point.
The problem I have is that I cannot write the derivative value to a variable out of scope. Trying to return a value from inside the canvas fails.

Here is my code:

#import "@preview/cetz:0.4.0"
#set page(width: auto, height: auto, margin: .5cm)



// I want the value to be here
#let derivative = (0, 0)

#cetz.canvas({
  import cetz.draw: *
  import cetz.vector: *


  // sample point from where to get the derivative
  // important for my use case
  let sample = (2, 2)

  // get intersection close to the sample
  intersections("i", {
    hide(circle(sample, radius: 10e-5))
    catmull((2, 2), (2.2, 2.8), (4.4, 4), (4, 4.8), tension: 0.4)
  })

  // loop over the one intersection
  for-each-anchor("i", (name) => {
    group(ctx => {
        let (ctx, origin) = cetz.coordinate.resolve(ctx, ("i." + name))

        let d = sub(origin, sample)
        let n = norm(d)

        // does not work because of the scope
        // derivative = n
        
        line(sample, add(sample, scale(n, 0.3)), stroke: red)
    })
  })
})