- #1
charmedbeauty
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Homework Statement
Find dy/dx in terms of x and y if..
x2-√(xy)+y2=6
Homework Equations
The Attempt at a Solution
so I started by..
x2-√(xy)+y2=6
deriving the LHS
2x+2y(dy/dx)-1/2(xy)-1/2(1(y)+x(dy/dx))
Simplifying the last term
2x+2y(dy/dx)-(y+x(dy/dx))/(2√(xy))=6
taking the 2x over to separate dy/dx's
2y(dy/dx)-(y+x(dy/dx))/(2√(xy))= 6-2x
then I thought I would multiply through to get a common denominator..
[2y(dy/dx)(2√(xy))-(y+x(dy/dx))] / [2√(xy) =6 -2x
so multiply through by denominator to simplify and collect like terms
[2y(dy/dx)(2√(xy))-(y+x(dy/dx))] = (6-2x)(2√(xy))
so taking that -y over
[2y(dy/dx)(2√(xy))-(x(dy/dx))]= (6-2x)(2√(xy))+y
taking out dy/dx as a common factor
dy/dx[4y√(xy) - x] = (6-2x)(2√(xy))+y
so dy/dx = [(6-2x)(2√(xy))+y] / [4y√(xy) - x]
Is this right, because I checked it on wolfram and it had a different answer so I guess not, can someone please shed some light on where I went wrong?
Thanks.