I am teaching the chain rule to a student in high school and was thinking about the possibility to justify the chain rule using (but not just by means of them) the cancellation process (which I am aware it is not a totally correct way to see it). I mean if, beyond the algebraic process of the cancellation, is it possible to improve the insight of it relating it with proportionality and compound ratios. Do anyone else see the bridge in a clear and compact way?
Thanks.