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Can anyone help me finding the derivative of x^2+4xy+y^2=6
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# Can anyone help me finding the derivative of x^2+4xy+y^2=6

[From: ] [author: ] [Date: 11-05-16] [Hit: ]
......
i have to find y'. Its implicit differentiation
answer me as soon as possible

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x^2 + 4xy + y^2 = 6
2x * dx + 4x * dy + 4y * dx + 2y * dy = 0
x * dx + 2x * dy + 2y * dx + y * dy = 0
dy * (y + 2x) + dx * (x + 2y) = 0
dy * (y + 2x) = -dx * (x + 2y)
dy/dx = -(x + 2y) / (y + 2x)

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Given:
x² + 4xy + y² = 6

Take the derivative:
2x + 4[xy' + y] + 2yy' = 0
2x + 4xy' + 4y + 2yy' = 0

Subtract 2x and 4y:
4xy' + 2yy' = -2x − 4y

Factor out y':
y'(4x + 2y) = -2x − 4y

Divide:
y' = -(2x + 4y)/(4x + 2y)
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