If y is a function of x and (x+y)=2 x y , then the value of y^ (0) is

Step-by-step solution

(x+y)=2 x y...(i) Differentiating both sides w.r.t. x , we get aligned & ( 1 x+y ) (1+ d y ~d x )=2 (x ~d y ~d x +y ) & d y ~d x = 1-2 x y-2 y^2 2 x^2+2 x y-1 aligned Putting x=0 in (i), we get aligned & y=1 & y^ (0)= 1-0-2 0+0-1 =1 aligned