i have to find y'. Its implicit differentiation
answer me as soon as possible
answer me as soon as possible

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)
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)

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)
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)