Question

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

Answer 1

... @ (0,1/2)

Answer 2

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

Answer 3

alright give me a second to remember lol

Answer 4

alright i'll upload a picture on what to do

Answer 5

and an example give me a sec

Answer 6

cool thanks

Answer 7

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

Answer 8

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

Answer 9

by factor

Answer 10

right righ tok so and

Answer 11

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

Answer 12

let me get a piece of paper lol

Answer 13

ama differentiate for u

Answer 14

thanks k cool coco

Answer 15

love it

Answer 16

so is coco checking if your differentiation is right?

Answer 17

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

Answer 18

i'm guessing

Answer 19

oh, ok

Answer 20

yes

Answer 21

ouch

Answer 22

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?

Answer 23

yeah i got completely something else than he did

Answer 24

the second is a chain and the first is just regular

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

yes

Answer 29

\[2yy'-8yy'=6x-2\]

Answer 30

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

Answer 31

yep

Answer 32

then you can pull out y'

Answer 33

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

Answer 34

the - is outside parenthesis

Answer 35

\[-(6x-2)/6y\]

Answer 36

it's been a while though lol

Answer 37

blah wait i messed up lol

Answer 38

let me do this all over agani

Answer 39

i forgot something

Answer 40

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

Answer 41

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?

Answer 42

my chain rule was messed up lol it should be

\[2x+2yy'=2(2x^2+2y^2-x)(4x+4yy'-1)\]

Answer 43

yes
that's what i got

Answer 44

then what did you do

Answer 45

i'd say to combine the right side

Answer 46

it's going to be ugly hahah

Answer 47

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

Answer 48

divide*

Answer 49

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

Answer 50

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

Answer 51

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

Answer 52

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

Answer 53

it's not that bad tho

Answer 54

Oh, ok. thanks!

Answer 55

\[2x+2yy'=16x^3+16y^3y'+16x^2yy'+16y^2x-12x^2-4y^2-8xyy'+2x\]
\[2yy'=16x^3+16^3y'+16x^2yy'+16y^2x-12x^2-4y^2-8xyy'\]

Answer 56

...

Answer 57

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

Answer 58

what

Answer 59

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

Answer 60

what you multiply that whole thing by dy/dx too

Answer 61

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

Answer 62

what did you get damn

Answer 63

using the chain rule i got

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

Answer 64

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

Answer 65

yeahhhh

Answer 66

alright so if you combine the terms on the right

Answer 67

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

Answer 68

idk that's gay

Answer 69

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.

Answer 70

not done yet haha

Answer 71

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

Answer 72

unless your teacher is crazy and solved for like y lol

Answer 73

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

Answer 74

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