There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}}}}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}}}}\right)}{dx}\\=&(\frac{(\frac{((\frac{(\frac{((\frac{(\frac{((\frac{(\frac{((\frac{(\frac{((\frac{(\frac{((\frac{(\frac{((\frac{(\frac{(0)}{(1)} - \frac{(1)log_{x}^{1}}{(x)})}{(ln(x))}))}{(log_{x}^{1})} - \frac{(1)log_{x}^{log_{x}^{1}}}{(x)})}{(ln(x))}))}{(log_{x}^{log_{x}^{1}})} - \frac{(1)log_{x}^{log_{x}^{log_{x}^{1}}}}{(x)})}{(ln(x))}))}{(log_{x}^{log_{x}^{log_{x}^{1}}})} - \frac{(1)log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}{(x)})}{(ln(x))}))}{(log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}})} - \frac{(1)log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}}{(x)})}{(ln(x))}))}{(log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}})} - \frac{(1)log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}}}{(x)})}{(ln(x))}))}{(log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}})} - \frac{(1)log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}}}}{(x)})}{(ln(x))}))}{(log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}}})} - \frac{(1)log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}}}}}{(x)})}{(ln(x))})\\=&\frac{-1}{xlog(x, log_{x}^{1})log(x, log_{x}^{log_{x}^{1}})log(x, log_{x}^{log_{x}^{log_{x}^{1}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}})ln^{8}(x)} - \frac{1}{xlog(x, log_{x}^{log_{x}^{1}})log(x, log_{x}^{log_{x}^{log_{x}^{1}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}})ln^{7}(x)} - \frac{1}{xlog(x, log_{x}^{log_{x}^{log_{x}^{1}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}})ln^{6}(x)} - \frac{1}{xlog(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}})ln^{5}(x)} - \frac{1}{xlog(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}})log(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}})ln^{4}(x)} - \frac{1}{xlog(x, log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}})ln^{3}(x)} - \frac{1}{xln^{2}(x)} - \frac{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{log_{x}^{1}}}}}}}}}{xln(x)}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!