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

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