1. By: Susana Cardona & Demetri Cheatham © Cardona & Cheatham 2011

2.  Slope of a tangent line  Six different techniques: Chain rule, product rule, Quotient rule, E.T.A, Implicit differentiation and Logs.

3. Chain Rule Bring exponent down in front of the variable, if it’s a coefficient multiply exponent. Then subtract one from the exponent and go back in and take a derivative.

4. Example

5. Try Me

6. Solution

7. Product Rule  First write the problem times derivative of the second problem plus write the second problem times the derivative of the first problem.  FDS+SDF

8. Example    

9. Try Me 

10. Solution 

11. Quotient Rule Write the bottom times the derivative of the top minus write the top times the derivative of the bottom over the bottom squared

12. Example

13. Try Me ◦

14. Solution

15.  Bring down exponent, multiply coefficient if there’s one, and write the trig and the angle times the derivative of the trig times the derivative of the angle

16. 1. 2.

17. 

18. 

19. N ATURAL L OG 1 over the angle times the derivative of the angle

20. E XAMPLE

21. TRY ME

22. S OLUTION

23. Implicit Is almost the same as a chain rule but it includes x and y and the x’s and y’s can be separated

24. Example

25. Try Me

26. Solution

29. OR