There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(xsin(x)sqrt(1 - {e}^{x}))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(xsin(x)sqrt(-{e}^{x} + 1))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(xsin(x)sqrt(-{e}^{x} + 1))\right)}{dx}\\=&\frac{(sin(x)sqrt(-{e}^{x} + 1) + xcos(x)sqrt(-{e}^{x} + 1) + \frac{xsin(x)(-({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 0)*\frac{1}{2}}{(-{e}^{x} + 1)^{\frac{1}{2}}})*\frac{1}{2}}{(xsin(x)sqrt(-{e}^{x} + 1))^{\frac{1}{2}}}\\=&\frac{sin^{\frac{1}{2}}(x)sqrt(-{e}^{x} + 1)^{\frac{1}{2}}}{2x^{\frac{1}{2}}} + \frac{x^{\frac{1}{2}}cos(x)sqrt(-{e}^{x} + 1)^{\frac{1}{2}}}{2sin^{\frac{1}{2}}(x)} - \frac{x^{\frac{1}{2}}{e}^{x}sin^{\frac{1}{2}}(x)}{4(-{e}^{x} + 1)^{\frac{1}{2}}sqrt(-{e}^{x} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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