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

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