Chain rule, second derivatives

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

On your own