What is the derivative dy/dx of y^2 + 2y + 2xy + x^2 + 4 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to find the derivative `dy/dx ` of y^2 + 2y + 2xy + x^2 + 4 = 0

Use implicit differentiation.

`(d(y^2 + 2y + 2xy + x^2 + 4))/dx = 0`

=> `(2y*(dy/dx) + 2*(dy/dx) + 2x*(dy/dx) + 2y + 2x) = 0`

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

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

=> `dy/dx = (-y - x)/(1 + x + y)`

The required derivative `dy/dx = (-x - y)/(1 +x +y)`

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