There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({(2022*2021)}^{-1})ln(\frac{e^{2022x}}{(e^{2022x} + 2021)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{4086462}ln(\frac{e^{2022x}}{(e^{2022x} + 2021)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{4086462}ln(\frac{e^{2022x}}{(e^{2022x} + 2021)})\right)}{dx}\\=&\frac{\frac{1}{4086462}((\frac{-(e^{2022x}*2022 + 0)}{(e^{2022x} + 2021)^{2}})e^{2022x} + \frac{e^{2022x}*2022}{(e^{2022x} + 2021)})}{(\frac{e^{2022x}}{(e^{2022x} + 2021)})}\\=&\frac{-e^{2022x}}{2021(e^{2022x} + 2021)} + \frac{1}{2021}\\ \end{split}\end{equation} \]

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