[m]\frac{x^{\frac{1}{x}-1}}{x}=\frac{x^{\frac{1}{x}}\cdot x^{-1}}{x}=\frac{x^{\frac{1}{x}}}{x^2}[/m]
[m]\frac{x^{\frac{1}{x}-1}}{x}-\frac{x^{\frac{1}{x}}\cdot ln(x)}{x^2}=\frac{x^{\frac{1}{x}}}{x^2}-\frac{x^{\frac{1}{x}}\cdot ln(x)}{x^2}=\frac{x^{\frac{1}{x}}\cdot(1- ln(x))}{x^2}=[/m]
[m]=\frac{1}{x^2}\cdot x^{\frac{1}{x}}\cdot(lne- ln(x))=x^{\frac{1}{x}-2}ln\frac{e}{x}[/m]