Small Group Activity: Finding a Chain Rule

Surfaces/Bridge Workshop 2023
Students use chain rule diagrams to construct a multivariable chain rule in terms of differentials.
What students learn
  • When you “zap with \(d\)” without having an explicit function, you need to name the coefficients of the differentials.
  • The coefficients of differentials obtained by “zapping with \(d\)” are derivatives, either ordinary derivatives or partial derivatives.
  • The difference in notation between ordinary derivatives with straight \(d\)s and partial derivatives with curly \(\partial\)s.

Given unknown functions \(f(x,y)\), \(x(t)\), and \(y(t)\), write the differential \(df\) of \(f\) in terms of \(dt\).

Keywords
Learning Outcomes