What is the derivative dy/dx for y^2 + x^2 = 8xy - 14y

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The derivative `dy/dx` has to be determined given that y^2 + x^2 = 8xy - 14y. Use implicit differentiation here.

Take the derivative with respect to x of both the sides. This gives:

`2*y(dy/dx) + 2x = 8y + 8x*(dy/dx) - 14(dy/dx)`

=> `(dy/dx)(2y - 8x + 14) = 8y - 2x`

=> `dy/dx = (8y - 2x)/(2y - 8x + 14)`

=> `dy/dx = (4y - x)/(y - 4x + 7)`

The derivative `dy/dx` for the given relation is `dy/dx = (4y - x)/(y - 4x + 7)`

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