`"If "y=sqrt(cosx+sqrt(cosx+sqrt(cosx+...oo)))", prove that "(dy)/(dx)=(sinx)/((2y-1)).

If y=sqrt(cos x+sqrt(cos x +sqrt(cos x+....oo))) " then prove that " dy/dx = sinx /(1-2y).

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

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ tooo))),p rov et h a t(dy)/(dx)=(cosx)/(2y-1)

If y=sqrt(x+sqrt(x+sqrt(x+longrightarrow oo))), prove that (dy)/(dx)=(1)/(2y-1)

If y=sqrt(x+sqrt(x+sqrt(+…..oo))) then prove that (2y-1)dy/dx=1.

If y=(cosx)^((((cosx)^(((cosx)^((...oo)) prove that (dy)/(dx)=-(y^2tanx)/(1-ylogcosx)

If y=sqrt(sinx+sqrt(sinx+sqrt(sinx+ . . .oo))) , then (dy)/(dx) is equal to

"If "y=(sinx)^(cosx)+(cosx)^(sinx)", prove that "(dy)/(dx)=(sinx)^(cosx).[cot x cos x-sin x(log sinx)]+(cosx)^(sinx).[cosx(log cos x)-sinx tanx].

Solve: (dy)/(dx)+y=cosx-sinx

If y=(cos x)^((cosx)^((cos x )...oo)) then prove that dy/dx=(y^2 tan x)/(y log (cosx)-1).