1. Chain Rule

2. Power Rule
Product Rule
Quotient Rule

3. We are not able to take the derivative of these functions with the power, product and quotient rules.
We will be able to take the derivative of these functions using the Chain Rule
To use the Chain Rule the function needs to be broken up into two functions. The next slides will demonstrate how to break up a function to use the chain rule.

4. I will divide these steps into two parts
If I plug in a number for x what happens to it?
Multiplied by 2
Add 3
Squared
I will divide these steps into two parts

5. The part of f(x) that does the first two steps is
Multiplied by 2
Add 3
Square

6. The part of f(x) that does the third step is
Multiplied by 2
Add 3
Square

7. This is the inside function
Multiplied by 2
Add 3
Square
This is the outside function

8. What is the derivative of the inside function?
This is the inside function
What is the derivative of the inside function?
What is the derivative of the outside function?
This is the outside function

9. Inside= d(Inside)= Outside= d(Outside)=
Find the inside function and outside function then find the derivative of each
Inside=
d(Inside)=
Outside=
d(Outside)=

10. Inside= d(Inside)= Outside= d(Outside)=
Find the inside function and outside function then find the derivative of each
Inside=
d(Inside)=
Outside=
d(Outside)=

11. Inside= d(Inside)= Outside= d(Outside)=
Find the inside function and outside function then find the derivative of each
Inside=
d(Inside)=
Outside=
d(Outside)=

12. The chain rule is
This means
The Derivative of a Composite Function is: The derivative of the outside function leaving the inside function alone, times the derivative of the inside function

14. The derivative of the outside function leaving the inside function alone times the derivative of the inside function
Derivative of inside function
Inside=
d(Inside)=
Outside=
Derivative of outside function leaving inside function alone
d(Outside)=

15. Inside= d(Inside)= Outside= d(Outside)=
Derivative of inside function
Inside=
Derivative of outside function leaving inside function alone
d(Inside)=
Outside=
d(Outside)=

16. Lets try some on our own.

17. P ,7,8

18. Inside= d(Inside)= Outside= d(Outside)=
Derivative of inside function
Inside=
d(Inside)=
Derivative of inside function leaving inside function alone
Outside=
d(Outside)=

19. When the last thing to happen is multiplication we need to use the product rule
Use the chain rule to find the derivative of the 2nd
1st
2nd =
d(1st )=3
d(2nd )

20. When the last thing to happen is division we need to use the quotient rule
Lo=
d(Hi)=
d(Lo)=

22. Lets try some on our own.

23. P ,13,15,16

24. To find the derivative of the inside function I need to use the chain rule a second time.

26. P ,14,17-20