2.3 The product rule, quotient rule, and higher order derivatives

1. 2.3 The product rule, quotient rule, and higher order derivatives "Life is too short for long division."

2. Objective

3. Derivative Rules • Constant Rule • Power Rule • Constant Multiple Rule • Derivative of x lemma • Trig Rules • Sum and Difference Rule

4. Limit Rules • Sum and difference of limits • Product of limits • Quotient of limits

5. What about…

6. Product Rule • The derivative of the product of 2 differentiable functions f and g is differentiable. Specifically: • In other words, • h’(x) = (derivative of the first) times (second) + (derivative of the second) times (first)

7. Example

8. Another example

9. One more example

10. Quotient Rule • The derivative of f/g of 2 differentiable functions f and g is differentiable at all values as long as g(x) =/ 0. Specifically: • In other words:

11. Example

12. Another example

13. One more example

14. More trig rules

15. Still more

16. Try…

17. Higher Order Derivatives • You can take more than one derivative • Position function  Velocity function  Acceleration function

18. Example • Find y ‘’