There are 1 questions in this calculation: for each question, the 4 derivative of o is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ log_{o}^{{o}^{2}}\ with\ respect\ to\ o：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = log_{o}^{o^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( log_{o}^{o^{2}}\right)}{do}\\=&(\frac{(\frac{(2o)}{(o^{2})} - \frac{(1)log_{o}^{o^{2}}}{(o)})}{(ln(o))})\\=&\frac{2}{oln(o)} - \frac{log_{o}^{o^{2}}}{oln(o)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2}{oln(o)} - \frac{log_{o}^{o^{2}}}{oln(o)}\right)}{do}\\=&\frac{2*-1}{o^{2}ln(o)} + \frac{2*-1}{oln^{2}(o)(o)} - \frac{-log_{o}^{o^{2}}}{o^{2}ln(o)} - \frac{(\frac{(\frac{(2o)}{(o^{2})} - \frac{(1)log_{o}^{o^{2}}}{(o)})}{(ln(o))})}{oln(o)} - \frac{log_{o}^{o^{2}}*-1}{oln^{2}(o)(o)}\\=&\frac{-2}{o^{2}ln(o)} - \frac{4}{o^{2}ln^{2}(o)} + \frac{log_{o}^{o^{2}}}{o^{2}ln(o)} + \frac{2log_{o}^{o^{2}}}{o^{2}ln^{2}(o)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2}{o^{2}ln(o)} - \frac{4}{o^{2}ln^{2}(o)} + \frac{log_{o}^{o^{2}}}{o^{2}ln(o)} + \frac{2log_{o}^{o^{2}}}{o^{2}ln^{2}(o)}\right)}{do}\\=&\frac{-2*-2}{o^{3}ln(o)} - \frac{2*-1}{o^{2}ln^{2}(o)(o)} - \frac{4*-2}{o^{3}ln^{2}(o)} - \frac{4*-2}{o^{2}ln^{3}(o)(o)} + \frac{-2log_{o}^{o^{2}}}{o^{3}ln(o)} + \frac{(\frac{(\frac{(2o)}{(o^{2})} - \frac{(1)log_{o}^{o^{2}}}{(o)})}{(ln(o))})}{o^{2}ln(o)} + \frac{log_{o}^{o^{2}}*-1}{o^{2}ln^{2}(o)(o)} + \frac{2*-2log_{o}^{o^{2}}}{o^{3}ln^{2}(o)} + \frac{2(\frac{(\frac{(2o)}{(o^{2})} - \frac{(1)log_{o}^{o^{2}}}{(o)})}{(ln(o))})}{o^{2}ln^{2}(o)} + \frac{2log_{o}^{o^{2}}*-2}{o^{2}ln^{3}(o)(o)}\\=&\frac{4}{o^{3}ln(o)} + \frac{12}{o^{3}ln^{2}(o)} + \frac{12}{o^{3}ln^{3}(o)} - \frac{2log_{o}^{o^{2}}}{o^{3}ln(o)} - \frac{6log_{o}^{o^{2}}}{o^{3}ln^{2}(o)} - \frac{6log_{o}^{o^{2}}}{o^{3}ln^{3}(o)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{4}{o^{3}ln(o)} + \frac{12}{o^{3}ln^{2}(o)} + \frac{12}{o^{3}ln^{3}(o)} - \frac{2log_{o}^{o^{2}}}{o^{3}ln(o)} - \frac{6log_{o}^{o^{2}}}{o^{3}ln^{2}(o)} - \frac{6log_{o}^{o^{2}}}{o^{3}ln^{3}(o)}\right)}{do}\\=&\frac{4*-3}{o^{4}ln(o)} + \frac{4*-1}{o^{3}ln^{2}(o)(o)} + \frac{12*-3}{o^{4}ln^{2}(o)} + \frac{12*-2}{o^{3}ln^{3}(o)(o)} + \frac{12*-3}{o^{4}ln^{3}(o)} + \frac{12*-3}{o^{3}ln^{4}(o)(o)} - \frac{2*-3log_{o}^{o^{2}}}{o^{4}ln(o)} - \frac{2(\frac{(\frac{(2o)}{(o^{2})} - \frac{(1)log_{o}^{o^{2}}}{(o)})}{(ln(o))})}{o^{3}ln(o)} - \frac{2log_{o}^{o^{2}}*-1}{o^{3}ln^{2}(o)(o)} - \frac{6*-3log_{o}^{o^{2}}}{o^{4}ln^{2}(o)} - \frac{6(\frac{(\frac{(2o)}{(o^{2})} - \frac{(1)log_{o}^{o^{2}}}{(o)})}{(ln(o))})}{o^{3}ln^{2}(o)} - \frac{6log_{o}^{o^{2}}*-2}{o^{3}ln^{3}(o)(o)} - \frac{6*-3log_{o}^{o^{2}}}{o^{4}ln^{3}(o)} - \frac{6(\frac{(\frac{(2o)}{(o^{2})} - \frac{(1)log_{o}^{o^{2}}}{(o)})}{(ln(o))})}{o^{3}ln^{3}(o)} - \frac{6log_{o}^{o^{2}}*-3}{o^{3}ln^{4}(o)(o)}\\=&\frac{-12}{o^{4}ln(o)} - \frac{44}{o^{4}ln^{2}(o)} - \frac{72}{o^{4}ln^{3}(o)} - \frac{48}{o^{4}ln^{4}(o)} + \frac{6log_{o}^{o^{2}}}{o^{4}ln(o)} + \frac{22log_{o}^{o^{2}}}{o^{4}ln^{2}(o)} + \frac{36log_{o}^{o^{2}}}{o^{4}ln^{3}(o)} + \frac{24log_{o}^{o^{2}}}{o^{4}ln^{4}(o)}\\ \end{split}\end{equation} \]

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