There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {lg(x)}^{5}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = lg^{5}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg^{5}(x)\right)}{dx}\\=&\frac{5lg^{4}(x)}{ln{10}(x)}\\=&\frac{5lg^{4}(x)}{xln{10}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{5lg^{4}(x)}{xln{10}}\right)}{dx}\\=&\frac{5*-lg^{4}(x)}{x^{2}ln{10}} + \frac{5*-0lg^{4}(x)}{xln^{2}{10}} + \frac{5*4lg^{3}(x)}{xln{10}ln{10}(x)}\\=&\frac{-5lg^{4}(x)}{x^{2}ln{10}} + \frac{20lg^{3}(x)}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-5lg^{4}(x)}{x^{2}ln{10}} + \frac{20lg^{3}(x)}{x^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{-5*-2lg^{4}(x)}{x^{3}ln{10}} - \frac{5*-0lg^{4}(x)}{x^{2}ln^{2}{10}} - \frac{5*4lg^{3}(x)}{x^{2}ln{10}ln{10}(x)} + \frac{20*-2lg^{3}(x)}{x^{3}ln^{2}{10}} + \frac{20*-2*0lg^{3}(x)}{x^{2}ln^{3}{10}} + \frac{20*3lg^{2}(x)}{x^{2}ln^{2}{10}ln{10}(x)}\\=&\frac{10lg^{4}(x)}{x^{3}ln{10}} - \frac{60lg^{3}(x)}{x^{3}ln^{2}{10}} + \frac{60lg^{2}(x)}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{10lg^{4}(x)}{x^{3}ln{10}} - \frac{60lg^{3}(x)}{x^{3}ln^{2}{10}} + \frac{60lg^{2}(x)}{x^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{10*-3lg^{4}(x)}{x^{4}ln{10}} + \frac{10*-0lg^{4}(x)}{x^{3}ln^{2}{10}} + \frac{10*4lg^{3}(x)}{x^{3}ln{10}ln{10}(x)} - \frac{60*-3lg^{3}(x)}{x^{4}ln^{2}{10}} - \frac{60*-2*0lg^{3}(x)}{x^{3}ln^{3}{10}} - \frac{60*3lg^{2}(x)}{x^{3}ln^{2}{10}ln{10}(x)} + \frac{60*-3lg^{2}(x)}{x^{4}ln^{3}{10}} + \frac{60*-3*0lg^{2}(x)}{x^{3}ln^{4}{10}} + \frac{60*2lg(x)}{x^{3}ln^{3}{10}ln{10}(x)}\\=&\frac{-30lg^{4}(x)}{x^{4}ln{10}} + \frac{220lg^{3}(x)}{x^{4}ln^{2}{10}} - \frac{360lg^{2}(x)}{x^{4}ln^{3}{10}} + \frac{120lg(x)}{x^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]

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