There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(sqrt(sqrt(\frac{xln(x)}{ln({x}^{x})})))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(sqrt(sqrt(\frac{xln(x)}{ln({x}^{x})})))\right)}{dx}\\=&\frac{(\frac{ln(x)}{ln({x}^{x})} + \frac{x}{(x)ln({x}^{x})} + \frac{xln(x)*-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{ln^{2}({x}^{x})({x}^{x})})*\frac{1}{2}*\frac{1}{2}*\frac{1}{2}}{(\frac{xln(x)}{ln({x}^{x})})^{\frac{1}{2}}(sqrt(\frac{xln(x)}{ln({x}^{x})}))^{\frac{1}{2}}(sqrt(sqrt(\frac{xln(x)}{ln({x}^{x})})))^{\frac{1}{2}}}\\=&\frac{ln^{\frac{1}{2}}(x)}{8x^{\frac{1}{2}}ln^{\frac{1}{2}}({x}^{x})sqrt(\frac{xln(x)}{ln({x}^{x})})^{\frac{1}{2}}sqrt(sqrt(\frac{xln(x)}{ln({x}^{x})}))^{\frac{1}{2}}} + \frac{1}{8x^{\frac{1}{2}}ln^{\frac{1}{2}}(x)ln^{\frac{1}{2}}({x}^{x})sqrt(\frac{xln(x)}{ln({x}^{x})})^{\frac{1}{2}}sqrt(sqrt(\frac{xln(x)}{ln({x}^{x})}))^{\frac{1}{2}}} - \frac{x^{\frac{1}{2}}ln^{\frac{3}{2}}(x)}{8ln^{\frac{3}{2}}({x}^{x})sqrt(\frac{xln(x)}{ln({x}^{x})})^{\frac{1}{2}}sqrt(sqrt(\frac{xln(x)}{ln({x}^{x})}))^{\frac{1}{2}}} - \frac{x^{\frac{1}{2}}ln^{\frac{1}{2}}(x)}{8ln^{\frac{3}{2}}({x}^{x})sqrt(\frac{xln(x)}{ln({x}^{x})})^{\frac{1}{2}}sqrt(sqrt(\frac{xln(x)}{ln({x}^{x})}))^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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