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If `y=x^(x)`, what is `(dy)/(dx)` at x = 1 equal to?

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If `y=x^(x)`, what is `(dy)/(dx)` at x = 1 equal to?
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Let `y = x^(x)`
Take log on both the sides
`rArr lny = x . Lny`
`rArr (1)/(y).(dy)/(dx)=1 + ln x rArr (1)/(y).(dy)/(dx) = lne + lnx`
`rArr (dy)/(dx)=y^(lnex=)=(x^(x))lnex`
`(dy)/(dx)|_(x=1)=1. lne = 1`
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