1. Implicit Differentiation - Used in cases where it is impossible to solve for “y” as an explicit function of “x”

2. Implicit Differentiation - Used in cases where it is impossible to solve for “y” as an explicit function of “x”

3. Implicit Differentiation - Used in cases where it is impossible to solve for “y” as an explicit function of “x”

4. Implicit Differentiation

5. OK, here is how I like to attack these :

6. Implicit Differentiation OK, here is how I like to attack these : - get your x’s and number together and take the derivative

7. Implicit Differentiation OK, here is how I like to attack these : - get your x’s and number together and take the derivative

8. Implicit Differentiation OK, here is how I like to attack these : - get your x’s and number together and take the derivative - get the y’s together and take the derivative

9. Implicit Differentiation OK, here is how I like to attack these : - get your x’s and number together and take the derivative - get the y’s together and take the derivative

10. Implicit Differentiation

14. this is the derivative

15. Implicit Differentiation

16. Let’s get it in standard form :

17. Implicit Differentiation Let’s get it in standard form :

18. Implicit Differentiation Let’s get it in standard form : - get your x’s and number together and take the derivative

19. Implicit Differentiation Let’s get it in standard form : - get your y’s together and take the derivative

20. Implicit Differentiation Let’s get it in standard form :

21. Implicit Differentiation Let’s get it in standard form :

22. Implicit Differentiation Let’s get it in standard form :

23. Implicit Differentiation Let’s get it in standard form :

24. Implicit Differentiation Let’s get it in standard form : - This is your derivative

25. Implicit Differentiation

29. - Use a and b again like we did with complex functions and the product rule…

30. Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

31. Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

32. Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

33. Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

34. Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

35. Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

36. Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

37. Implicit Differentiation - Use a and b again like we did with complex functions and the product rule…

38. Implicit Differentiation - Use a and b again like we did with complex functions and the product rule… - When you can, you should simplify as far as possible…

39. Implicit Differentiation

49. - again, you should simplify as far as possible…

50. Implicit Differentiation Now substitute your ( - 5, 17 ) into your derivative to find the slope of the tangent line…