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## Homework Statement

Find the derivative of y=x

^{1/x}

## Homework Equations

Chain rule and logarithmic differentiation.

## The Attempt at a Solution

y=x^(1/x)

lny=lnx^(1/x)

lny=(1/x)lnx

(1/y)y'=(1/x)lnx

y'=y((1/x)lnx)

y'=y((1/x)(1/x)+(lnx)(1/x))

y'=y((1/x^2)+(lnx/x))

y'=x^(1/x)((1/x^2)+(lnx/x))

Sorry for all the brackets, and if they are not correct :$