1.

`(log x)^(log x),x gt1`

Answer» Let `y=(log x)^(log x)`
`implieslogy=log[(log x)^(log x)]=logx*log(logx)`
Differentiate both sides w.r.t. x
`(1)/(y)(dy)/(dx)=logx*(d)/(dx)log(logx)+log(logx)(d)/(dx)logx`
`=logx*(1)/(logx)*(d)/(dx)logx+log(logx)*(1)/(x)`
`implies (dy)/(dx)=y[(1)/(x)+(1)/(x)log(logx)]`
`=(logx)^(logx)[(1)/(x)+(1)/(x)log(logx)]`


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