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

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