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

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