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

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