There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {x}^{3} + {lg(x)}^{2} + 4{x}^{2} + ln(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{3} + lg^{2}(x) + 4x^{2} + ln(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{3} + lg^{2}(x) + 4x^{2} + ln(x)\right)}{dx}\\=&3x^{2} + \frac{2lg(x)}{ln{10}(x)} + 4*2x + \frac{1}{(x)}\\=&\frac{2lg(x)}{xln{10}} + 3x^{2} + 8x + \frac{1}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2lg(x)}{xln{10}} + 3x^{2} + 8x + \frac{1}{x}\right)}{dx}\\=&\frac{2*-lg(x)}{x^{2}ln{10}} + \frac{2*-0lg(x)}{xln^{2}{10}} + \frac{2}{xln{10}ln{10}(x)} + 3*2x + 8 + \frac{-1}{x^{2}}\\=&\frac{-2lg(x)}{x^{2}ln{10}} + \frac{2}{x^{2}ln^{2}{10}} + 6x - \frac{1}{x^{2}} + 8\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2lg(x)}{x^{2}ln{10}} + \frac{2}{x^{2}ln^{2}{10}} + 6x - \frac{1}{x^{2}} + 8\right)}{dx}\\=&\frac{-2*-2lg(x)}{x^{3}ln{10}} - \frac{2*-0lg(x)}{x^{2}ln^{2}{10}} - \frac{2}{x^{2}ln{10}ln{10}(x)} + \frac{2*-2}{x^{3}ln^{2}{10}} + \frac{2*-2*0}{x^{2}ln^{3}{10}} + 6 - \frac{-2}{x^{3}} + 0\\=&\frac{4lg(x)}{x^{3}ln{10}} - \frac{6}{x^{3}ln^{2}{10}} + \frac{2}{x^{3}} + 6\\ \end{split}\end{equation} \]

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