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BITSAT2020MathematicsDifferentiationActual

If x y+y²= x+y, then find d y d x is

Options

  1. A² x x+2 y
  2. B² x-y (x+2 y-1)
  3. C(x+2 y-1) ² x
  4. D² x y

Correct answer

B. ² x-y (x+2 y-1)

Step-by-step solution

The given relation is x y+y²= x+y . Differentiating both sides with respect to x , we get d d x (x y)+ d d x (y² )= d d x ( x)+ d y d x or [y 1+x d y d x ]+2 y d y d x = ² x+ d y d x or (x+2 y-1) d y d x = ² x-y d y d x = ² x-y (x+2 y-1)

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