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

2. Theorem 13.6 Chain Rule: One Independent Variable and Figure 13.39

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

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

5. Theorem 13.7 Chain Rule: Two Independent Variables and Figure 13.41

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

7. Theorem 13.8 Chain Rule: Implicit Differentiation