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

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