## calyne 3 years ago Use implicit differentiation to find an equation of the tangent line to the curve at the curve at the given point: x^2 + y^2 = (2x^2 + 2y^2 - x)^2

1. calyne

... @ (0,1/2)

2. calyne

not that i tmatters anyway i'm just a little confused regarding the differentiation here

3. Outkast3r09

alright give me a second to remember lol

4. Outkast3r09

alright i'll upload a picture on what to do

5. Outkast3r09

and an example give me a sec

6. calyne

cool thanks

7. calyne

like i got as far as [4x+4y*y']/[4x+4y*y'-1] = 2x^2 + 2y^2 - x

8. Outkast3r09

actualy i can't... i'll just type it out what my book says GUIDELINES FOR IMPLICIT DIFFERENTIATION 1. Differentiat both sides of the equatio with respects to x 2. collect al terms involve dy/dx on the left side of the equation and move all others to right 3.factor dy/dx out of the left side of the equation 4.solve for dy/dx by dividing both sides

9. Outkast3r09

by factor

10. calyne

right righ tok so and

11. calyne

so what do i do from what i have am i good so far

12. Outkast3r09

let me get a piece of paper lol

13. cococupcoffee

ama differentiate for u

14. calyne

thanks k cool coco

15. calyne

love it

16. Outkast3r09

so is coco checking if your differentiation is right?

17. cococupcoffee

one question. just verifying... for the secon part, everyting is raised to teh 2nd power?

18. Outkast3r09

i'm guessing

19. cococupcoffee

oh, ok

20. Outkast3r09

yes

21. cococupcoffee

ouch

22. cococupcoffee

umm. i suck @ algebra... and i think i am going to mess up if i do this. but, i am still going to go ahead and square all that. can someone then tell me if i was right?

23. Outkast3r09

yeah i got completely something else than he did

24. Outkast3r09

the second is a chain and the first is just regular

25. Outkast3r09

i got 2x+2yy'=2(4x+4yy'-1)

26. Outkast3r09

=2x+2yy'= 8x+8yy'-2

27. cococupcoffee

if you do implicit differentiation, then don't you do (for example, the first part): 2xdx+2ydy... then get all teh dx's and dy's on one side and divide so that dy/dx

28. Outkast3r09

yes

29. Outkast3r09

$2yy'-8yy'=6x-2$

30. cococupcoffee

ahh... i get it.. am so stupid! i was wondering where you got the chain rule from

31. Outkast3r09

yep

32. Outkast3r09

then you can pull out y'

33. Outkast3r09

i think it's$\frac{-6x-2}{6y}$

34. Outkast3r09

the - is outside parenthesis

35. Outkast3r09

$-(6x-2)/6y$

36. Outkast3r09

it's been a while though lol

37. Outkast3r09

blah wait i messed up lol

38. Outkast3r09

let me do this all over agani

39. Outkast3r09

i forgot something

40. Outkast3r09

it doesn't help that i'm also trying to help two people

41. cococupcoffee

ok, sorry guys but i am lost lol. but i wanna know how it's done. so outkast, once you did the chain rule, did you multiply or what?

42. Outkast3r09

my chain rule was messed up lol it should be $2x+2yy'=2(2x^2+2y^2-x)(4x+4yy'-1)$

43. cococupcoffee

yes that's what i got

44. cococupcoffee

then what did you do

45. Outkast3r09

i'd say to combine the right side

46. Outkast3r09

it's going to be ugly hahah

47. cococupcoffee

dive 2xdx + 2ydy with 4xdx+4ydy...?

48. cococupcoffee

divide*

49. Outkast3r09

i think you'd have to combine the right side which is a pain

50. cococupcoffee

Hey, do you know is there anyway i can like mark this question so that i can come back and look @ it 2morrow?

51. cococupcoffee

no seriously?! ouch... calyne, your proff/teacher must be coldhearted to give you such a question.

52. Outkast3r09

um i think it should still be in the top left forner under notifications

53. Outkast3r09

it's not that bad tho

54. cococupcoffee

Oh, ok. thanks!

55. Outkast3r09

$2x+2yy'=16x^3+16y^3y'+16x^2yy'+16y^2x-12x^2-4y^2-8xyy'+2x$ $2yy'=16x^3+16^3y'+16x^2yy'+16y^2x-12x^2-4y^2-8xyy'$

56. calyne

...

57. Outkast3r09

did you get what me and coco got about my last when you used the chain rule

58. calyne

what

59. calyne

you use the chain rule yeah du^2/du * du/dx first thing overall ik

60. calyne

what you multiply that whole thing by dy/dx too

61. Outkast3r09

so whta did you get after you take dy/dx of both sides

62. calyne

what did you get damn

63. Outkast3r09

using the chain rule i got 2x+2yy'=2(2x^2+2y^2-x)(4x+4yy'-1)

64. calyne

sorry i got 2x+2yy' = 2(2x^2+2y^2-x) (4x + 4yy' - 1)

65. calyne

yeahhhh

66. Outkast3r09

alright so if you combine the terms on the right

67. Outkast3r09

is what i did ... what did you do after

68. calyne

idk that's gay

69. calyne

i tried a bunch of different stuff what was your final answer i'll tell you if it's correct nah flutter that the answer is x+1/2. is that what you got. if not we're wasting time.

70. Outkast3r09

not done yet haha

71. Outkast3r09

yeah i have no idea.. even wolfram alpha has omething like my end answer

72. Outkast3r09

unless your teacher is crazy and solved for like y lol

73. Outkast3r09

wait the answer to the differentiation is that or the tangent line

74. Outkast3r09

because if it's the tangent line my implicit differentiation may be correct