Derivitive of x^(1/x)

If y=x^(1/x), what's dy/dx

ln y= (1/x)ln(x)
1/y (dy/dx)=-x^-2*ln(x)+(1/x)(1/x)
(1/y)(dy/dx)=-ln(x)/x^2+1/x^2
(1/y)(dy/dx)=(1-ln(x))/x^2
(dy/dx)=y(1-ln(x))/x^2