If `y=x^x^x^^((((oo))))`, find `(dy)/(dx)dot`

1.	If `y=x^x^x^^((((oo))))`, find `(dy)/(dx)dot`
Answer» `y=x^(y)` `"or "log y = y log x` `"or "(1)/(y)(dy)/(dx)=(dy)/(dx)xxlog x+y(1)/(x)" "[Diff. both sides w.r.t.x]` `"or "(dy)/(dx)({1-y log x })/(y)=(y)/(x)` `"or "(dy)/(dx)=(y^(2))/(x(1-y log x))`

Discussion

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