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

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