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

Your problem has not been solved here? Please take a look at the  hot problems ！