There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ log_{log_{log_{2}^{1}}^{log_{2}^{2}}}^{log_{log_{2}^{3}}^{log_{2}^{4}}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{log_{log_{2}^{1}}^{log_{2}^{2}}}^{log_{log_{2}^{3}}^{log_{2}^{4}}}\right)}{dx}\\=&(\frac{(\frac{((\frac{(\frac{((\frac{(\frac{(0)}{(4)} - \frac{(0)log_{2}^{4}}{(2)})}{(ln(2))}))}{(log_{2}^{4})} - \frac{((\frac{(\frac{(0)}{(3)} - \frac{(0)log_{2}^{3}}{(2)})}{(ln(2))}))log_{log_{2}^{3}}^{log_{2}^{4}}}{(log_{2}^{3})})}{(ln(log_{2}^{3}))}))}{(log_{log_{2}^{3}}^{log_{2}^{4}})} - \frac{((\frac{(\frac{((\frac{(\frac{(0)}{(2)} - \frac{(0)log_{2}^{2}}{(2)})}{(ln(2))}))}{(log_{2}^{2})} - \frac{((\frac{(\frac{(0)}{(1)} - \frac{(0)log_{2}^{1}}{(2)})}{(ln(2))}))log_{log_{2}^{1}}^{log_{2}^{2}}}{(log_{2}^{1})})}{(ln(log_{2}^{1}))}))log_{log_{log_{2}^{1}}^{log_{2}^{2}}}^{log_{log_{2}^{3}}^{log_{2}^{4}}}}{(log_{log_{2}^{1}}^{log_{2}^{2}})})}{(ln(log_{log_{2}^{1}}^{log_{2}^{2}}))})\\=&0\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]

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