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

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