1. The Product and Quotient Rules

2. If you recall, our formula for slope is defined as:
we can also write this as:
Therefore:
Therefore:
can be written as:

3. Let:
Then:
You can see this relationship by looking at the following diagram:

4. So:

5. Therefore, if then:
This is called the Product Rule

6. Find the derivative of:
Answer:

7. Find the derivative of:
Answer:

8. Find the derivative of:
Answer:
Find the derivative of:
Answer:

9. Let:
Then:
If:
Then:

10. This is called the Quotient Rule

11. Find the derivative of:
Answer:
Find the derivative of:
Answer:

12. Find the derivative of:
Answer:
Find the derivative of:
Answer:

13. Find the derivative of:
Answer:
Find the derivative of:
Answer:
Find the derivative of:
Answer:
Find the derivative of:
Answer:

14. Find the derivative of:
Answer:
Find the derivative of:
Answer:

15. Find the coordinates of any stationary points on the following curves and state the nature of each:
Answer: Max at (1, 256), Min at (5, 0)