1. The Product Rule
The derivative of the product of two differentiable functions is differentiable and is the first function times the derivative of the second function plus the second function times the derivative of the first function.
First
Second
First
Derivative of the Second
Second
Derivative of the First

2. Product Rule Example WRONG Find the derivative of First Second First
Derivative of the
Second
Second
Derivative of the
First

3. More Product Rule Examples
Constant
Multiple
Rule
That was
easy
This is not as difficult as I thought it would be. I better push the easy button.

4. Homework
Page 126: 1 – 6 All

5. That’s gonna be hard to remember.
The Quotient Rule
The derivative of the quotient of two differentiable functions is differentiable and is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared.
That’s gonna be hard to remember.

6. Remembering the Quotient Rule
Thank you, thank you very much.
Low
D-High
High
D-Low
Low Squared
That sounds like a song.
Low, d-high minus high, d-low over low squared.

7. Quotient Rule Example
High
Find the derivative of
Low
That was
easy

8. And Now the Hard One
That was easy

9. Homework
Page 126: 7 – 12 All

10. Derivatives of Trigonometric Functions
First, let’s review the ones that we already know.
Now, let’s look at some new ones.
I’d like to see you prove those.

11. Proof of the Derivative of a Trigonometric Function

12. Proof of the Derivative of a Trigonometric Function

13. Another Proof of the Derivative of a Trigonometric Function

14. Another Proof of the Derivative of a Trigonometric Function

15. One More Hard One

16. Homework
Page 126: 40 – 54 Even Numbers

17. Prove the following derivatives
Classwork
Prove the following derivatives