There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({2022}^{-2})ln(\frac{e^{2022}x}{(e^{2022}x + 2021)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{4088484}ln(\frac{xe^{2022}}{(xe^{2022} + 2021)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{4088484}ln(\frac{xe^{2022}}{(xe^{2022} + 2021)})\right)}{dx}\\=&\frac{\frac{1}{4088484}((\frac{-(e^{2022} + xe^{2022}*0 + 0)}{(xe^{2022} + 2021)^{2}})xe^{2022} + \frac{e^{2022}}{(xe^{2022} + 2021)} + \frac{xe^{2022}*0}{(xe^{2022} + 2021)})}{(\frac{xe^{2022}}{(xe^{2022} + 2021)})}\\=&\frac{-e^{2022}}{4088484(xe^{2022} + 2021)} + \frac{1}{4088484x}\\ \end{split}\end{equation} \]

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