Chain Rules for Functions of Several Variables Section 13.5 Chain Rules for Functions of Several Variables

Theorem 13.6 Chain Rule: One Independent Variable and Figure 13.39

Examples Find using the appropriate Chain Rule. 1) 2)

Example Differentiate implicitly to find the first partial derivatives of w.

Theorem 13.7 Chain Rule: Two Independent Variables and Figure 13.41

Example: Find and using the appropriate Chain Rule w=xcosyz

Theorem 13.8 Chain Rule: Implicit Differentiation