1. 3.4 Chain Rule

2. Prerequisite Knowledge Product Rule Quotient Rule Power Rule Special Derivatives:

3. Special Derivatives

4. Chain Rule with Numbers

5. Chain Rule With Calculus Why is this helpful? Suppose you had to differentiate:

6. Example:

7. Examples

8. Chain Rule Some special derivatives that come from the Chain Rule:

9. Homework Pg. 162 # 55-92 [6]

10. Applications (Day 2) Example: Air is being pumped into a spherical balloon so that the radius is increasing at a rate of 2 inches per second. At what rate is the volume increasing after 3 seconds? After 10 seconds?

11. Example 2 A 15 foot tall pole that was initially vertical begins to fall in such a way that the angle relative to the ground is decreasing at a rate of 3 degrees per second. At what rate is the top of the pole getting closer to the ground after 4 seconds?

12. Homework (2) Pg. 164 # 160-162

13. Homework (3) Pg. 164 # 163, 165