1. Lesson: Derivative Techniques -1
Obj – The Product & Quotient Rules

2. Example: Differentiate
When the Power Rule Fails:
Example: Differentiate

3. The problem with this situation is that the
function we are trying to differentiate is
a combination of two functions.
For situations like this, there are two
techniques that can be used to differentiate
the function.
The Product Rule
The Quotient Rule

4. An easier to remember version of the Product Rule is:

5. Some, however, prefer to write it as:
But, where did the Product Rule come from?

6. Proof of Product Rule

8. Q.E.D.
Quod Erat Demonstrandum,
Which means “Thus it is demonstrated”.

9. Ex. 1: Find if
Method 1: FOIL & Differentiate

10. Method 2: “Product Rule”g f

12. Ex. 2: Find if

13. Ex. 3: Differentiate

14. An easier to remember version of the Quotient Rule is:

15. Proof of Quotient Rule:

18. Q.E.D.

19. Ex. 4: Differentiate f g

22. Ex. 5: Find
(a)
(b) Where does the function
above have horizontal
tangent lines?

23. Ex. 6: For , Find

24. Ex. 7:
The table above gives values of the differentiable functions f and g and their derivatives at x = 3.
If h(x) = (3 f(x) + 2)(5 - g(x)), then h'(3) =

25. Ex. 8: find dy/dx, where d is a constant.

26. Ex. 9: Given the graphs of f and g below: If

27. HW: Product & Quotient Rule HW