## calyne Group Title 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 2 years ago 2 years ago

1. calyne Group Title

... @ (0,1/2)

2. calyne Group Title

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

3. Outkast3r09 Group Title

alright give me a second to remember lol

4. Outkast3r09 Group Title

alright i'll upload a picture on what to do

5. Outkast3r09 Group Title

and an example give me a sec

6. calyne Group Title

cool thanks

7. calyne Group Title

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

8. Outkast3r09 Group Title

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 Group Title

by factor

10. calyne Group Title

right righ tok so and

11. calyne Group Title

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

12. Outkast3r09 Group Title

let me get a piece of paper lol

13. cococupcoffee Group Title

ama differentiate for u

14. calyne Group Title

thanks k cool coco

15. calyne Group Title

love it

16. Outkast3r09 Group Title

so is coco checking if your differentiation is right?

17. cococupcoffee Group Title

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

18. Outkast3r09 Group Title

i'm guessing

19. cococupcoffee Group Title

oh, ok

20. Outkast3r09 Group Title

yes

21. cococupcoffee Group Title

ouch

22. cococupcoffee Group Title

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 Group Title

yeah i got completely something else than he did

24. Outkast3r09 Group Title

the second is a chain and the first is just regular

25. Outkast3r09 Group Title

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

26. Outkast3r09 Group Title

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

27. cococupcoffee Group Title

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 Group Title

yes

29. Outkast3r09 Group Title

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

30. cococupcoffee Group Title

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

31. Outkast3r09 Group Title

yep

32. Outkast3r09 Group Title

then you can pull out y'

33. Outkast3r09 Group Title

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

34. Outkast3r09 Group Title

the - is outside parenthesis

35. Outkast3r09 Group Title

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

36. Outkast3r09 Group Title

it's been a while though lol

37. Outkast3r09 Group Title

blah wait i messed up lol

38. Outkast3r09 Group Title

let me do this all over agani

39. Outkast3r09 Group Title

i forgot something

40. Outkast3r09 Group Title

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

41. cococupcoffee Group Title

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 Group Title

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

43. cococupcoffee Group Title

yes that's what i got

44. cococupcoffee Group Title

then what did you do

45. Outkast3r09 Group Title

i'd say to combine the right side

46. Outkast3r09 Group Title

it's going to be ugly hahah

47. cococupcoffee Group Title

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

48. cococupcoffee Group Title

divide*

49. Outkast3r09 Group Title

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

50. cococupcoffee Group Title

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 Group Title

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

52. Outkast3r09 Group Title

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

53. Outkast3r09 Group Title

54. cococupcoffee Group Title

Oh, ok. thanks!

55. Outkast3r09 Group Title

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

56. calyne Group Title

...

57. Outkast3r09 Group Title

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

58. calyne Group Title

what

59. calyne Group Title

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

60. calyne Group Title

what you multiply that whole thing by dy/dx too

61. Outkast3r09 Group Title

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

62. calyne Group Title

what did you get damn

63. Outkast3r09 Group Title

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

64. calyne Group Title

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

65. calyne Group Title

yeahhhh

66. Outkast3r09 Group Title

alright so if you combine the terms on the right

67. Outkast3r09 Group Title

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

68. calyne Group Title

idk that's gay

69. calyne Group Title

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 Group Title

not done yet haha

71. Outkast3r09 Group Title

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

72. Outkast3r09 Group Title

unless your teacher is crazy and solved for like y lol

73. Outkast3r09 Group Title

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

74. Outkast3r09 Group Title

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