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

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