The Quotient Rule

1. The Quotient Rule

2. Objective • To use the quotient rule for differentiation. • ES: Explicitly assessing information and drawing conclusions

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

4. The Quotient Rule NO Does ?

5. The Quotient Rule The derivative of a quotient is not necessarily equal to the quotient of the derivatives.

6. The Quotient Rule • The derivative of a quotient must by calculated using the quotient rule: Low d High minus High d Low, allover Low Low (low squared)

7. The Quotient Rule 1. Imagine that the function is actually broken into 2 pieces, high and low.

8. The Quotient Rule 2. In the numerator of a fraction, leave low piece alone and derive high piece.

9. The Quotient Rule 3. Subtract: Leave high piece alone and derive low piece.

10. The Quotient Rule 4. In the denominator: Square low piece. This is the derivative!

11. The Quotient Rule Final Answer

12. The Quotient Rule Low d High minus High d Low, allover Low Low (low squared)

13. Low d High minus High d Low, allover Low Low (low squared) Example A: Find the derivative Final Answer

14. Example B: Find the derivative Low d High minus High d Low, allover Low Low (low squared) Final Answer

15. Example C: Find the derivative Low d High minus High d Low, allover Low Low (low squared) Final Answer

16. Example D: Find the derivative Low d High minus High d Low, allover Low Low (low squared) Final Answer

17. Example E: Find the derivative Low d High minus High d Low, allover Low Low (low squared) Product Rule for D’Hi

18. The Quotient Rule Final Answer

19. The Quotient Rule • Remember: The derivative of a quotient is Low, D-High, minus High, D-Low, all over the bottom squared.