Hello,
[tex]y=x^{ \frac{1}{x}}* \dfrac{1-ln(x)}{x^2} \\\\
y=x^{ \frac{1}{x} -2}* (1-ln(x))\\\\
ln(y)= (\dfrac{1}{x} -2})*ln(x)+ln(1-ln(x))\\\\
\dfrac{d(ln(x))}{dx} = \dfrac{1}{y} * \dfrac{dy}{dx} \\
=- \frac{1}{x^2}*ln(x)+( \frac{1}{x}-2)* \frac{1}{x} + \frac{1}{1-ln(x)} *(- \frac{1}{x} )\\\\
\dfrac{dy}{dx}=(x^{ \frac{1}{x}}* \dfrac{1-ln(x)}{x^2}) *(\frac{-1}{x^2}*ln(x)+( \frac{1}{x}-2)* \frac{1}{x} + \frac{1}{1-ln(x)} *\frac{-1}{x} )\\\\
...
[/tex]
I let you simplify.
