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If y=x^x^x^^((((oo)))) , find (dy)/(dx)d...

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

Text Solution

Verified by Experts

`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))`
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