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

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