There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {lg(x)}^{23456789}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = lg^{23456789}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg^{23456789}(x)\right)}{dx}\\=&\frac{23456789lg^{23456788}(x)}{ln{10}(x)}\\=&\frac{23456789lg^{23456788}(x)}{xln{10}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{23456789lg^{23456788}(x)}{xln{10}}\right)}{dx}\\=&\frac{23456789*-lg^{23456788}(x)}{x^{2}ln{10}} + \frac{23456789*-0lg^{23456788}(x)}{xln^{2}{10}} + \frac{23456789*23456788lg^{23456787}(x)}{xln{10}ln{10}(x)}\\=&\frac{-23456789lg^{23456788}(x)}{x^{2}ln{10}} + \frac{550220926733732lg^{23456787}(x)}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-23456789lg^{23456788}(x)}{x^{2}ln{10}} + \frac{550220926733732lg^{23456787}(x)}{x^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{-23456789*-2lg^{23456788}(x)}{x^{3}ln{10}} - \frac{23456789*-0lg^{23456788}(x)}{x^{2}ln^{2}{10}} - \frac{23456789*23456788lg^{23456787}(x)}{x^{2}ln{10}ln{10}(x)} + \frac{550220926733732*-2lg^{23456787}(x)}{x^{3}ln^{2}{10}} + \frac{550220926733732*-2*0lg^{23456787}(x)}{x^{2}ln^{3}{10}} + \frac{550220926733732*23456787lg^{23456786}(x)}{x^{2}ln^{2}{10}ln{10}(x)}\\=&\frac{46913578lg^{23456788}(x)}{x^{3}ln{10}} - \frac{1650662780201196lg^{23456787}(x)}{x^{3}ln^{2}{10}} - \frac{6305770260928892116lg^{23456786}(x)}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{46913578lg^{23456788}(x)}{x^{3}ln{10}} - \frac{1650662780201196lg^{23456787}(x)}{x^{3}ln^{2}{10}} - \frac{6305770260928892116lg^{23456786}(x)}{x^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{46913578*-3lg^{23456788}(x)}{x^{4}ln{10}} + \frac{46913578*-0lg^{23456788}(x)}{x^{3}ln^{2}{10}} + \frac{46913578*23456788lg^{23456787}(x)}{x^{3}ln{10}ln{10}(x)} - \frac{1650662780201196*-3lg^{23456787}(x)}{x^{4}ln^{2}{10}} - \frac{1650662780201196*-2*0lg^{23456787}(x)}{x^{3}ln^{3}{10}} - \frac{1650662780201196*23456787lg^{23456786}(x)}{x^{3}ln^{2}{10}ln{10}(x)} - \frac{6305770260928892116*-3lg^{23456786}(x)}{x^{4}ln^{3}{10}} - \frac{6305770260928892116*-3*0lg^{23456786}(x)}{x^{3}ln^{4}{10}} - \frac{6305770260928892116*23456786lg^{23456785}(x)}{x^{3}ln^{3}{10}ln{10}(x)}\\=&\frac{-140740734lg^{23456788}(x)}{x^{4}ln{10}} + \frac{6052430194071052lg^{23456787}(x)}{x^{4}ln^{2}{10}} + \frac{941133418154249464lg^{23456786}(x)}{x^{4}ln^{3}{10}} - \frac{7596301620547639016lg^{23456785}(x)}{x^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]

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