There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ log_{5}^{log_{5}^{log_{5}^{log_{5}^{log}}}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{5}^{log_{5}^{log_{5}^{log_{5}^{log}}}}\right)}{dx}\\=&(\frac{(\frac{((\frac{(\frac{((\frac{(\frac{((\frac{(\frac{(0)}{(log)} - \frac{(0)log_{5}^{log}}{(5)})}{(ln(5))}))}{(log_{5}^{log})} - \frac{(0)log_{5}^{log_{5}^{log}}}{(5)})}{(ln(5))}))}{(log_{5}^{log_{5}^{log}})} - \frac{(0)log_{5}^{log_{5}^{log_{5}^{log}}}}{(5)})}{(ln(5))}))}{(log_{5}^{log_{5}^{log_{5}^{log}}})} - \frac{(0)log_{5}^{log_{5}^{log_{5}^{log_{5}^{log}}}}}{(5)})}{(ln(5))})\\=& - \frac{0}{5}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{0}{5}\right)}{dx}\\=& - 0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 0\right)}{dx}\\=& - 0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - 0\right)}{dx}\\=& - 0\\ \end{split}\end{equation} \]

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