There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sin(x)sqrt(cos(2x)) + \frac{(sin(2x)cos(x))}{sqrt(cos(2x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin(x)sqrt(cos(2x)) + \frac{sin(2x)cos(x)}{sqrt(cos(2x))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(x)sqrt(cos(2x)) + \frac{sin(2x)cos(x)}{sqrt(cos(2x))}\right)}{dx}\\=&cos(x)sqrt(cos(2x)) + \frac{sin(x)*-sin(2x)*2*\frac{1}{2}}{(cos(2x))^{\frac{1}{2}}} + \frac{cos(2x)*2cos(x)}{sqrt(cos(2x))} + \frac{sin(2x)*-sin(x)}{sqrt(cos(2x))} + \frac{sin(2x)cos(x)*--sin(2x)*2*\frac{1}{2}}{(cos(2x))(cos(2x))^{\frac{1}{2}}}\\=&cos(x)sqrt(cos(2x)) - \frac{sin(2x)sin(x)}{cos^{\frac{1}{2}}(2x)} + \frac{2cos(2x)cos(x)}{sqrt(cos(2x))} - \frac{sin(x)sin(2x)}{sqrt(cos(2x))} + \frac{sin^{2}(2x)cos(x)}{cos^{\frac{3}{2}}(2x)}\\ \end{split}\end{equation} \]

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