The Product Rule

1. The Product Rule Today, students will analyze a proof of the Product Rule and learn when to apply the Product Rule

2. Today, you are going to find the derivative of functions of the form j(x)=f(x)·g(x). Some of these are easy to do using algebra to expand ahead of time: Do you notice any patterns?

3. Try some more difficult cases: Do you notice any patterns?

4. Let’s consider a function that’s not easy to expand: It would be nice to develop a method to differentiate the product of two functions. Explain how the function above can be modeled as j(x)=f(x)·g(x).

5. The Derivative of a Product When Hana looked at the function j(x)=f(x)·g(x) she immediately thought of a rectangle whose length and width were f(x) and g(x)and whose area was j(x).Hana would like to find j’(x) by using the definition of the derivative as a limit.

6. The Derivative of a Product

7. The Derivative of a Product

8. The Derivative of a Product

9. The Derivative of a Product

10. Using your result:

11. This is the Product Rule:

12. Sneaky Product Rule Problems:

14. Assignment: • HW R • See you tmrrw!!!