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

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