99 Percentile Qs Bank for JEE MainMathematicsDifferentiation

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

Options

Ay^3-x 2 y^2-2 x y+1
Bx+y^3 2 y^2-x
Cy+x y^2-2 x
Dy^2-x 2 y^3-2 x y-1

Correct answer

D. y^2-x 2 y^3-2 x y-1

Step-by-step solution

We have aligned & y= x+ y+ x+ y+ & y= x+ y+y y^2=x+ 2 y & y^2-x= 2 y (y^2-x )^2=2 y & y^4-2 x y^2+x^2=2 y & y^4-2 x y^2-2 y+x^2=0 aligned On differentiating w.r.t. to x , we get aligned & 4 y^3 d y d x -2 y^2-4 y x d y d x - 2 d y d x +2 x=0 & d y d x (4 y^3-4 x y-2 )=-2 x+2 y^2 & d y d x = y^2-x 2 y^3-2 x y-1 aligned

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