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

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