Quotientenregel:
\(f(x):=\dfrac{u(x)}{v(x)} \rightarrow f'(x)=\dfrac{u'(x)\cdot v(x) - u(x) \cdot v'(x)}{v^2(x)}\\ u(x)=\ln x \rightarrow u'(x)=\dfrac{1}{x},\, v(x)=x \rightarrow v'(x)=1\)
Hier: \(\left [\dfrac{\ln x}{x}\right ]'=\dfrac{\frac{1}{x}\cdot x - \ln x \cdot 1}{x^2}=\dfrac{\frac{x}{x}-\ln x}{x^2}=\dfrac{1-\ln x}{x^2}\)