There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {log_{3}^{x}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {\left(log_{3}^{x}\right)}^{2}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {\left(log_{3}^{x}\right)}^{2}\right)}{dx}\\=&(\frac{2log_{3}^{x}(\frac{(1)}{(x)} - \frac{(0)log_{3}^{x}}{(3)})}{(ln(3))})\\=&\frac{2log_{3}^{x}}{xln(3)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2log_{3}^{x}}{xln(3)}\right)}{dx}\\=&\frac{2*-log_{3}^{x}}{x^{2}ln(3)} + \frac{2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{3}^{x}}{(3)})}{(ln(3))})}{xln(3)} + \frac{2log_{3}^{x}*-0}{xln^{2}(3)(3)}\\=&\frac{-2log_{3}^{x}}{x^{2}ln(3)} + \frac{2}{x^{2}ln^{2}(3)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2log_{3}^{x}}{x^{2}ln(3)} + \frac{2}{x^{2}ln^{2}(3)}\right)}{dx}\\=&\frac{-2*-2log_{3}^{x}}{x^{3}ln(3)} - \frac{2(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{3}^{x}}{(3)})}{(ln(3))})}{x^{2}ln(3)} - \frac{2log_{3}^{x}*-0}{x^{2}ln^{2}(3)(3)} + \frac{2*-2}{x^{3}ln^{2}(3)} + \frac{2*-2*0}{x^{2}ln^{3}(3)(3)}\\=&\frac{4log_{3}^{x}}{x^{3}ln(3)} - \frac{6}{x^{3}ln^{2}(3)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{4log_{3}^{x}}{x^{3}ln(3)} - \frac{6}{x^{3}ln^{2}(3)}\right)}{dx}\\=&\frac{4*-3log_{3}^{x}}{x^{4}ln(3)} + \frac{4(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{3}^{x}}{(3)})}{(ln(3))})}{x^{3}ln(3)} + \frac{4log_{3}^{x}*-0}{x^{3}ln^{2}(3)(3)} - \frac{6*-3}{x^{4}ln^{2}(3)} - \frac{6*-2*0}{x^{3}ln^{3}(3)(3)}\\=&\frac{-12log_{3}^{x}}{x^{4}ln(3)} + \frac{22}{x^{4}ln^{2}(3)}\\ \end{split}\end{equation} \]

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