**Learning objectives**

- Explore the chain rule for compositions of functions with various numbers of variables
- Interpret second derivatives in applied contexts
- Explore relations among partial derivatives
- Universal: Second mixed partials
- In modeling situations: some PDES

**Before class**

- Read Hughes-Hallett sections 14.6 and 14.7 (only pp 806-808)
- Ponder Hughes-Hallett problems: 14.6: 3, 9, 16, 19; 14.7: 1-6, 22-31, 50, 51.

**In class**

- Some chain rule problems
- Some second derivative problems
- Some PDEs

**On your own**

- Extensive and intensive variables in science