apa bentuk turunan dari Log ( x^(ln x) )?

[tex]\displaystyle f(x)=\log(x^{\ln x})\\f(x)=\log(e^{\ln x^{\ln x}})\\f(x)=\log(e^{\ln x\cdot \ln x})\\f(x)=\log(e^{\ln^2x})\\\\f'(x)=\frac{\frac{2\ln x}{x}}{e^{\ln^2x}\ln10}\\\boxed{\boxed{f'(x)=\frac{2\log x}{xe^{\ln^2x}}}}[/tex]