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

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