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

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