calyne
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
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calyne
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... @ (0,1/2)
calyne
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not that i tmatters anyway i'm just a little confused regarding the differentiation here
Outkast3r09
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alright give me a second to remember lol
Outkast3r09
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alright i'll upload a picture on what to do
Outkast3r09
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and an example give me a sec
calyne
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cool thanks
calyne
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like i got as far as [4x+4y*y']/[4x+4y*y'-1] = 2x^2 + 2y^2 - x
Outkast3r09
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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
Outkast3r09
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by factor
calyne
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right righ tok so and
calyne
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so what do i do from what i have am i good so far
Outkast3r09
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let me get a piece of paper lol
cococupcoffee
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ama differentiate for u
calyne
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thanks k cool coco
calyne
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love it
Outkast3r09
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so is coco checking if your differentiation is right?
cococupcoffee
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one question. just verifying... for the secon part, everyting is raised to teh 2nd power?
Outkast3r09
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i'm guessing
cococupcoffee
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oh, ok
Outkast3r09
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yes
cococupcoffee
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ouch
cococupcoffee
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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?
Outkast3r09
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yeah i got completely something else than he did
Outkast3r09
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the second is a chain and the first is just regular
Outkast3r09
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i got 2x+2yy'=2(4x+4yy'-1)
Outkast3r09
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=2x+2yy'= 8x+8yy'-2
cococupcoffee
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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
Outkast3r09
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yes
Outkast3r09
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\[2yy'-8yy'=6x-2\]
cococupcoffee
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ahh... i get it.. am so stupid! i was wondering where you got the chain rule from
Outkast3r09
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yep
Outkast3r09
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then you can pull out y'
Outkast3r09
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i think it's\[\frac{-6x-2}{6y}\]
Outkast3r09
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the - is outside parenthesis
Outkast3r09
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\[-(6x-2)/6y\]
Outkast3r09
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it's been a while though lol
Outkast3r09
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blah wait i messed up lol
Outkast3r09
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let me do this all over agani
Outkast3r09
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i forgot something
Outkast3r09
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it doesn't help that i'm also trying to help two people
cococupcoffee
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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?
Outkast3r09
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my chain rule was messed up lol it should be
\[2x+2yy'=2(2x^2+2y^2-x)(4x+4yy'-1)\]
cococupcoffee
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yes
that's what i got
cococupcoffee
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then what did you do
Outkast3r09
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i'd say to combine the right side
Outkast3r09
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it's going to be ugly hahah
cococupcoffee
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dive 2xdx + 2ydy with 4xdx+4ydy...?
cococupcoffee
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divide*
Outkast3r09
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i think you'd have to combine the right side which is a pain
cococupcoffee
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Hey, do you know is there anyway i can like mark this question so that i can come back and look @ it 2morrow?
cococupcoffee
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no seriously?! ouch... calyne, your proff/teacher must be coldhearted to give you such a question.
Outkast3r09
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um i think it should still be in the top left forner under notifications
Outkast3r09
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it's not that bad tho
cococupcoffee
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Oh, ok. thanks!
Outkast3r09
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\[2x+2yy'=16x^3+16y^3y'+16x^2yy'+16y^2x-12x^2-4y^2-8xyy'+2x\]
\[2yy'=16x^3+16^3y'+16x^2yy'+16y^2x-12x^2-4y^2-8xyy'\]
calyne
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...
Outkast3r09
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did you get what me and coco got about my last when you used the chain rule
calyne
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what
calyne
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you use the chain rule yeah du^2/du * du/dx first thing overall ik
calyne
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what you multiply that whole thing by dy/dx too
Outkast3r09
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so whta did you get after you take dy/dx of both sides
calyne
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what did you get damn
Outkast3r09
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using the chain rule i got
2x+2yy'=2(2x^2+2y^2-x)(4x+4yy'-1)
calyne
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sorry i got 2x+2yy' = 2(2x^2+2y^2-x) (4x + 4yy' - 1)
calyne
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yeahhhh
Outkast3r09
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alright so if you combine the terms on the right
Outkast3r09
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is what i did ... what did you do after
calyne
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idk that's gay
calyne
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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.
Outkast3r09
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not done yet haha
Outkast3r09
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yeah i have no idea.. even wolfram alpha has omething like my end answer
Outkast3r09
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unless your teacher is crazy and solved for like y lol
Outkast3r09
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wait the answer to the differentiation is that or the tangent line
Outkast3r09
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because if it's the tangent line my implicit differentiation may be correct