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

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