If y= x 1+ x 1+ x x , then dy dx is given by

Step-by-step solution

aligned & y= x 1+ x 1+ x 1+ x & y= x 1+ x 1+y aligned aligned & y= (1+y) x (1+y)+ x & y ((1+y)+ x)=(1+y) x & y+y^2+y x= x+ x y aligned Differentiating w.r.to x , we get d y ~d x +2 y ~d y ~d x +y(- x)+ x ~d y ~d x = d y ~d x x+(1+y) x aligned & d y ~d x +2 y ~d y ~d x -y x+ x ~d y ~d x & = x ~d y ~d x +(1+y) x & ~d y ~d x (1+2 y+ x- x) aligned = x+y x+y x d y ~d x = y x+(1+y) x 1+2 y+ x- x