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BITSAT2024MathematicsDifferentiationActual

If x 1+y +y 1+x =0 , then d y d x =

Options

  1. Ax+1 x
  2. B1 1+x
  3. C-1 (1+x)^2
  4. Dx 1+x

Correct answer

C. -1 (1+x)^2

Step-by-step solution

aligned & Given, x 1+y +y 1+x =0 & x 1+y =-y 1+x & (x 1+y )^2=(-y 1+x )^2 aligned array lr & x^2(1+y)=y^2(1+x) & x^2-y^2=y^2 x-x^2 y & (x-y)(x+y)=x y(y-x) & x+y=-x y & x+y+x y=0 & y= -x 1+x =-1+ 1 1+x array Differentiating w.r.t, x d y d x =- 1 (1+x)^2

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