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

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