" 3.If "y=x^(x^(x)cdots cdots^(oo))," prove that "x(dy)/(dx)=(y^(2))/(1-y log x)

Similar Questions

Explore conceptually related problems

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

If y=e^(x+e^(x+e^(x)+cdots*oo)), prove that (dy)/(dx)=(y)/(1-y)

If y=a^(x^(x^(2)*oo)), prove that (dy)/(dx)=(y^(2)log y)/(x(1-y log x*log y))

If y = x^y , prove that (dy)/(dx) = (y^2)/(x(1 - y log x))

Differentiate the following w.r.t.x. y = x^(x^(x^( oo))) , prove that x (dy)/(dx) = (y^2)/(1 - y log x)

"If "y=a^(x^(a^(x...oo)))", prove that "(dy)/(dx)=(y^(2)(logy))/(x[1-y(logx)(logy)]).

"If "y=a^(x^(a^(x...oo)))", prove that "(dy)/(dx)=(y^(2)(logy))/(x[1-y(logx)(logy)])

If y=(cos x)^(cos x)^^(((cos x)dot oo)), prove that (dy)/(dx)=-(y^(2)tan x)/((1-y log cos x))

If y^(x)=e^(y-x), prove that (dy)/(dx)=((1+log y)^(2))/(log y)