2. Mr. Miehl miehlm@tesd.net
The Product Rule
Mr. Miehl

3. Objective
To use the product rule for differentiation.

4. The Product Rule Good News: Right now you can find the
derivative of functions like …
A number multiplied by
a variable raised to a power.
Bad News: The Power Rule
doesn’t work for a lot of derivatives.

5. This function consists of
The Product Rule
This function consists of
two separate pieces
multiplied together

6. The Product Rule
What is the derivative of this function?

7. The Product Rule
Take each derivative
NO!
Does ?

8. The Product Rule
The derivative of a product is not equal to the product of the derivatives.

9. The Product Rule
1. Imagine that the function is actually broken into 2 pieces.

10. The Product Rule
2. Leave first piece alone and derive second piece.

11. The Product Rule
3. Add: Leave second piece alone and derive first piece.
This is the derivative!

12. The Product Rule

13. The Product Rule
The derivative of a product must by calculated using the product rule:

14. The Product Rule The derivative of a product is… the first times
the derivative of the second
plus the second times
the derivative of the first.

15. The Product Rule

16. The Product Rule

17. The Product Rule

18. The Product Rule

19. The Product Rule

20. Conclusion
Remember: The derivative of a product is the first times the derivative of the second plus the second times the derivative of the first.