\priklad{D}Zderivujte:
   $$
      y = \sqrt[x]{x} \quad (x>0).
   $$
   \reseni
   \begin{equation*}\begin{split}
      y'(x) &= {(x^{1/x})}'=x^{1/x}{\left(\frac1x\log x\right)}'
             = x^{1/x}{\left(\frac{\log x}x\right)}'
             = x^{1/x}\left(\frac{(1/x)x - \log x}{x^2}\right)=\\
            &= x^{1/x - 2}(1-\log x).
   \end{split}\end{equation*}