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QUICK, can someone explain to me how to implicitly differentiate this problem

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forfun
Posts: 4916 - Karma: 66
Ok so the problem is

x + xy + y = sin 2x

so i do implicit differentiation to both sides and get this as my answer...

y' = 2 cos 2x -2 / y

but i should be getting this...

y' = 2 cos 2x - 1 - y / x + 1

I thought i was taking the derivative of everything right and put in dy/dx for the y's, but i have no idea how they got to that answer, and my test is tomorrow!! ahhhhh
Dec 6 2006 1:06AM
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petek
Posts: 8762 - Karma: 12
I would tell you but then i'd have to kill you.
Dec 6 2006 1:09AM
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forfun
Posts: 4916 - Karma: 66
ooo good news now my answer looks like this...

y' = 2 cos 2x - 1 - y

but i still have no idea why it was divided by x + 1...

waaaa :( im so fuckin screwwwed
Dec 6 2006 1:13AM
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zerospinskier
Posts: 4867 - Karma: 350
im doing my french hw right now but...

x + xy + y = sin 2x

well can u get to this?

1 + 1y x xy' + y' = 2sin2x

then

yxy' + y' = 2sin2x - 1


im sick and cant think right now. so maybe someone else cna go from here
Dec 6 2006 1:17AM
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zerospinskier
Posts: 4867 - Karma: 350
ya i forgot to go to cos. man im sick right now.
Dec 6 2006 1:18AM
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i-like-to-ride
Posts: 17 - Karma: 10
x + xy + y = sin 2x
1 + y + xy' y' = 2cos2x
xy' + y' = 2cos2x - 1 - y
y'(x + 1) = 2cos2x - 1 - y
y' = (2cos2x - 1 - y)/(x + 1)

Hopefully that helps. First you implicitly differentiat and get all the y' to one side. then you factor out the y' and divide and you have your answer. Good luck fucker
Dec 6 2006 1:20AM
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forfun
Posts: 4916 - Karma: 66
soo i dont get where that x and xy' came from? is it chain rule or something?
Dec 6 2006 1:20AM
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zerospinskier
Posts: 4867 - Karma: 350
ya nvm, the x was actually supposed to be a +. just look at the guy above me. hes right
Dec 6 2006 1:24AM
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Elife
Posts: 2829 - Karma: 44
then factor out the y and divide by x+1
Dec 6 2006 3:08AM
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GFELLER.
Posts: 640 - Karma: 13
If you look hard enough, if you flip the y, it looks surprisingly similar to the Half Life logo, lambda.

Coincidence?
Click for larger image
Dec 6 2006 7:22AM
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