1. Lesson 2.3 Product & Quotient Rules and Higher Derivatives

2. Product Rule If a function is the product of 2 functions, the derivative is: 1 st ● (derivative of 2 nd ) + 2 nd ● (derivative of 1 st )

3. Example

4. Quotient Rule If a function is the quotient of 2 functions, the derivative is: [bottom ● (derivative of top) − top ● (derivative of bottom)] ÷ bottom 2

5. Mathematical Proofs: The Product Rule

6. Example

8. More Trig Derivatives

9. Draw the position of a ball rolling off a table: Now try to draw a graph of the velocity of the ball:

10. Finally, graph the acceleration of the ball:

11. Higher Order Derivatives s(t)position v(t) = s’(t)velocity a(t) = v’(t) = s’’(t)acceleration

13. Example Problem Set 2.3