There are 1 questions in this calculation: for each question, the 4 derivative of D is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ log_{D}^{e^{D}}\ with\ respect\ to\ D：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{D}^{e^{D}}\right)}{dD}\\=&(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})\\=&\frac{1}{ln(D)} - \frac{log_{D}^{e^{D}}}{Dln(D)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{ln(D)} - \frac{log_{D}^{e^{D}}}{Dln(D)}\right)}{dD}\\=&\frac{-1}{ln^{2}(D)(D)} - \frac{-log_{D}^{e^{D}}}{D^{2}ln(D)} - \frac{(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{Dln(D)} - \frac{log_{D}^{e^{D}}*-1}{Dln^{2}(D)(D)}\\=&\frac{-2}{Dln^{2}(D)} + \frac{log_{D}^{e^{D}}}{D^{2}ln(D)} + \frac{2log_{D}^{e^{D}}}{D^{2}ln^{2}(D)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2}{Dln^{2}(D)} + \frac{log_{D}^{e^{D}}}{D^{2}ln(D)} + \frac{2log_{D}^{e^{D}}}{D^{2}ln^{2}(D)}\right)}{dD}\\=&\frac{-2*-1}{D^{2}ln^{2}(D)} - \frac{2*-2}{Dln^{3}(D)(D)} + \frac{-2log_{D}^{e^{D}}}{D^{3}ln(D)} + \frac{(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{2}ln(D)} + \frac{log_{D}^{e^{D}}*-1}{D^{2}ln^{2}(D)(D)} + \frac{2*-2log_{D}^{e^{D}}}{D^{3}ln^{2}(D)} + \frac{2(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{2}ln^{2}(D)} + \frac{2log_{D}^{e^{D}}*-2}{D^{2}ln^{3}(D)(D)}\\=&\frac{3}{D^{2}ln^{2}(D)} + \frac{6}{D^{2}ln^{3}(D)} - \frac{2log_{D}^{e^{D}}}{D^{3}ln(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{2}(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{3}(D)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{3}{D^{2}ln^{2}(D)} + \frac{6}{D^{2}ln^{3}(D)} - \frac{2log_{D}^{e^{D}}}{D^{3}ln(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{2}(D)} - \frac{6log_{D}^{e^{D}}}{D^{3}ln^{3}(D)}\right)}{dD}\\=&\frac{3*-2}{D^{3}ln^{2}(D)} + \frac{3*-2}{D^{2}ln^{3}(D)(D)} + \frac{6*-2}{D^{3}ln^{3}(D)} + \frac{6*-3}{D^{2}ln^{4}(D)(D)} - \frac{2*-3log_{D}^{e^{D}}}{D^{4}ln(D)} - \frac{2(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{3}ln(D)} - \frac{2log_{D}^{e^{D}}*-1}{D^{3}ln^{2}(D)(D)} - \frac{6*-3log_{D}^{e^{D}}}{D^{4}ln^{2}(D)} - \frac{6(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{3}ln^{2}(D)} - \frac{6log_{D}^{e^{D}}*-2}{D^{3}ln^{3}(D)(D)} - \frac{6*-3log_{D}^{e^{D}}}{D^{4}ln^{3}(D)} - \frac{6(\frac{(\frac{(e^{D})}{(e^{D})} - \frac{(1)log_{D}^{e^{D}}}{(D)})}{(ln(D))})}{D^{3}ln^{3}(D)} - \frac{6log_{D}^{e^{D}}*-3}{D^{3}ln^{4}(D)(D)}\\=&\frac{-8}{D^{3}ln^{2}(D)} - \frac{24}{D^{3}ln^{3}(D)} - \frac{24}{D^{3}ln^{4}(D)} + \frac{6log_{D}^{e^{D}}}{D^{4}ln(D)} + \frac{22log_{D}^{e^{D}}}{D^{4}ln^{2}(D)} + \frac{36log_{D}^{e^{D}}}{D^{4}ln^{3}(D)} + \frac{24log_{D}^{e^{D}}}{D^{4}ln^{4}(D)}\\ \end{split}\end{equation} \]

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