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

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