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

Your problem has not been solved here? Please take a look at the  hot problems ！