This task is designed to promote good layout and logic with the chain rule. This is the formal, long approach. In my experience there is value in this, especially for pupils who will be pursuing more mathematics: the formal treatment relates closely with integration by substitution.

I haven’t been exhaustive here, but the task is designed to give 18 examples which pupils can draw upon for tackling a more routine exercise. All of the questions involved a single layer of chain rule. There are no examples such as y = (sin2x)^3 etc. As I wrote about in a recent blog for education Scotland, https://sites.google.com/eds.glow.scot/es-numeracymaths-blog/tasks-for-all-purposes-in-higher-mathematics, I have been trying to develop Higher tasks which can act as a set of notes, but are the work of the pupil – supported by me rather than done by me.

Credit: @chrismcgrane84