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

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