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

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