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If y=e^(x^(e ^(x^(...oo)))),show that,(d...

If `y=e^(x^(e ^(x^(...oo))))`,show that,`(dy)/(dx)=(y^(2)logy)/(x(1-y log x logy))`.

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x(dy)/(dx)=y(logy-logx-1)

(dy)/(dx)=e^(x-y)+1

(dy)/(dx)+1=e^(x-y)

(dy)/(dx)=e^(x-y)+x^(2)e^(-y)

If y=e^(x+e^(x+e^(x+....TOoo))) prove that dy/dx=y/((1-y))