There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ lg(x)lg(x)lg(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = lg^{3}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg^{3}(x)\right)}{dx}\\=&\frac{3lg^{2}(x)}{ln{10}(x)}\\=&\frac{3lg^{2}(x)}{xln{10}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{3lg^{2}(x)}{xln{10}}\right)}{dx}\\=&\frac{3*-lg^{2}(x)}{x^{2}ln{10}} + \frac{3*-0lg^{2}(x)}{xln^{2}{10}} + \frac{3*2lg(x)}{xln{10}ln{10}(x)}\\=&\frac{-3lg^{2}(x)}{x^{2}ln{10}} + \frac{6lg(x)}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3lg^{2}(x)}{x^{2}ln{10}} + \frac{6lg(x)}{x^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{-3*-2lg^{2}(x)}{x^{3}ln{10}} - \frac{3*-0lg^{2}(x)}{x^{2}ln^{2}{10}} - \frac{3*2lg(x)}{x^{2}ln{10}ln{10}(x)} + \frac{6*-2lg(x)}{x^{3}ln^{2}{10}} + \frac{6*-2*0lg(x)}{x^{2}ln^{3}{10}} + \frac{6}{x^{2}ln^{2}{10}ln{10}(x)}\\=&\frac{6lg^{2}(x)}{x^{3}ln{10}} - \frac{18lg(x)}{x^{3}ln^{2}{10}} + \frac{6}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6lg^{2}(x)}{x^{3}ln{10}} - \frac{18lg(x)}{x^{3}ln^{2}{10}} + \frac{6}{x^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{6*-3lg^{2}(x)}{x^{4}ln{10}} + \frac{6*-0lg^{2}(x)}{x^{3}ln^{2}{10}} + \frac{6*2lg(x)}{x^{3}ln{10}ln{10}(x)} - \frac{18*-3lg(x)}{x^{4}ln^{2}{10}} - \frac{18*-2*0lg(x)}{x^{3}ln^{3}{10}} - \frac{18}{x^{3}ln^{2}{10}ln{10}(x)} + \frac{6*-3}{x^{4}ln^{3}{10}} + \frac{6*-3*0}{x^{3}ln^{4}{10}}\\=&\frac{-18lg^{2}(x)}{x^{4}ln{10}} + \frac{66lg(x)}{x^{4}ln^{2}{10}} - \frac{36}{x^{4}ln^{3}{10}}\\ \end{split}\end{equation} \]

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