1. Sec 3.4: The Chain Rule
Composite function
Chain Rule:

2. Sec 3.4: The Chain Rule
Chain Rule:

3. Sec 3.4: The Chain Rule
Chain Rule:
Example:

4. Sec 3.4: The Chain Rule
Chain Rule:
Example:
Example:

5. Outer function is power Outer function is exponential
Sec 3.4: The Chain Rule
Chain Rule:
Special Case:
Outer function is power
Outer function is exponential
Outer funcion square root

6. Sec 3.4: The Chain Rule Example:
Chain THE POWER RULE COMBINED WITH THE CHAIN RULE:
Outer function is power
Example:

7. Sec 3.4: The Chain Rule Example: Example: Example:
Exponential COMBINED WITH THE CHAIN RULE:
Outer function is exponential
Example:
Example:
Example:

8. Sec 3.4: The Chain Rule Example: Example:
Exponential COMBINED WITH THE CHAIN RULE:
Example:
Example:

9. Sec 3.4: The Chain Rule

10. Sec 3.4: The Chain Rule Example: Example:
Square root COMBINED WITH THE CHAIN RULE:
Example:
Example:

11. Repeated Use of the Chain Rule
Sec 3.4: The Chain Rule
Repeated Use of the Chain Rule
Chain Rule:
Example:

12. Sec 3.4: The Chain Rule

13. Sec 3.4: The Chain Rule

14. Sec 3.4: The Chain Rule

15. Sec 3.4: The Chain Rule