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

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