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