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

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