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

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