There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ xsin(x){e}^{cos(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x{e}^{cos(x)}sin(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x{e}^{cos(x)}sin(x)\right)}{dx}\\=&{e}^{cos(x)}sin(x) + x({e}^{cos(x)}((-sin(x))ln(e) + \frac{(cos(x))(0)}{(e)}))sin(x) + x{e}^{cos(x)}cos(x)\\=&{e}^{cos(x)}sin(x) - x{e}^{cos(x)}sin^{2}(x) + x{e}^{cos(x)}cos(x)\\ \end{split}\end{equation} \]

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