If`y=sqrt(x+sqrt(x+sqrt(x+...oo)))`,show that, `(dy)/(dx)=(1)/(2y-1)`.

If y=(sqrt(x))^((sqrt(x))^((sqrt(x))^(...oo) , show that, x (dy)/(dx)=(y^(2))/(2-y log x).

If y=sqrt(sin x+sqrt(sinx+sqrt(sinx+…..oo))) show that (dy)/(dx) =(cos x )/(2y-1)

If y = sqrt(x+sqrt(x+sqrt(x+* * * infty))) then (dy)/(dx)=

If y="cot"^(-1) (sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)) , show that [(dy)/(dx)]_(x=(1)/(2))= -(1)/(sqrt(3)) .

If y=sqrt(logx+sqrt(logx+sqrt(logx+oo))),t h e n(dy)/(dx)i s (a) x/(2y-1) (b) x/(2y+1) (c) 1/(x(2y-1)) (d) 1/(x(1-2y))

(dy)/(dx)=sqrt(y-x)

(dy)/(dx)=sqrt(x+y+1)

"If "y=sqrt(x+sqrt(y+sqrt(x+sqrt(y+...oo))))," then prove that "(dy)/(dx)=(y^(2)-x)/(2y^(3)-2xy-1)

Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to (a) 1/(2y-1) (b) x/(x+2y) (c) 1/(sqrt(1+4x) (d) y/(2x+y)

If y=sqrt(x+sqrt(y+sqrt(x+sqrty+...oo))) then (dy)/(dx) equal to