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Find (dy)/(dx) when y= (x^(log x)) ( ...

Find ` (dy)/(dx) ` when ` y= (x^(log x)) ( log x)^(x), x gt 1`

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`log y = log [(x^(log x)) (log x)^(x)]`
` log y= log x^(log x) + log + (x) log log (x)`
`Rightarrow (dy)/(dx) = y[ 2 log x . 1/x + x . 1/(log x) . 1/x + log log x .1 ]`
`Rightarrow (dy)/(dx) = x^(log x). (log x)^(x) [ (2log x)/x + 1/(log x) + log log x]`
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