There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ x(3 + x){(ln(x))}^{2} + (x - 1)(x - 1 - 5ln(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 3xln^{2}(x) + x^{2}ln^{2}(x) - 5xln(x) + x^{2} - 2x + 5ln(x) + 1\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 3xln^{2}(x) + x^{2}ln^{2}(x) - 5xln(x) + x^{2} - 2x + 5ln(x) + 1\right)}{dx}\\=&3ln^{2}(x) + \frac{3x*2ln(x)}{(x)} + 2xln^{2}(x) + \frac{x^{2}*2ln(x)}{(x)} - 5ln(x) - \frac{5x}{(x)} + 2x - 2 + \frac{5}{(x)} + 0\\=&3ln^{2}(x) + ln(x) + 2xln^{2}(x) + 2xln(x) + 2x + \frac{5}{x} - 7\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3ln^{2}(x) + ln(x) + 2xln^{2}(x) + 2xln(x) + 2x + \frac{5}{x} - 7\right)}{dx}\\=&\frac{3*2ln(x)}{(x)} + \frac{1}{(x)} + 2ln^{2}(x) + \frac{2x*2ln(x)}{(x)} + 2ln(x) + \frac{2x}{(x)} + 2 + \frac{5*-1}{x^{2}} + 0\\=&\frac{6ln(x)}{x} + 2ln^{2}(x) + 6ln(x) + \frac{1}{x} - \frac{5}{x^{2}} + 4\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{6ln(x)}{x} + 2ln^{2}(x) + 6ln(x) + \frac{1}{x} - \frac{5}{x^{2}} + 4\right)}{dx}\\=&\frac{6*-ln(x)}{x^{2}} + \frac{6}{x(x)} + \frac{2*2ln(x)}{(x)} + \frac{6}{(x)} + \frac{-1}{x^{2}} - \frac{5*-2}{x^{3}} + 0\\=&\frac{-6ln(x)}{x^{2}} + \frac{4ln(x)}{x} + \frac{5}{x^{2}} + \frac{6}{x} + \frac{10}{x^{3}}\\ \end{split}\end{equation} \]

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