There are 1 questions in this calculation: for each question, the 4 derivative of o is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ lg_{o}^{e^{o}}\ with\ respect\ to\ o：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg_{o}^{e^{o}}\right)}{do}\\=&\frac{1}{ln{10}(o)}\\=&\frac{1}{oln{10}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{oln{10}}\right)}{do}\\=&\frac{-1}{o^{2}ln{10}} + \frac{-0}{oln^{2}{10}}\\=&\frac{-1}{o^{2}ln{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-1}{o^{2}ln{10}}\right)}{do}\\=&\frac{--2}{o^{3}ln{10}} - \frac{-0}{o^{2}ln^{2}{10}}\\=&\frac{2}{o^{3}ln{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2}{o^{3}ln{10}}\right)}{do}\\=&\frac{2*-3}{o^{4}ln{10}} + \frac{2*-0}{o^{3}ln^{2}{10}}\\=&\frac{-6}{o^{4}ln{10}}\\ \end{split}\end{equation} \]

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