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

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