There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{3(3sin(2x) + {(9{sin(2x)}^{2} + 40*7(cos(2x) + 1))}^{\frac{1}{2}})}{20}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{9}{20}sin(2x) + \frac{3}{20}(9sin^{2}(2x) + 280cos(2x) + 280)^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{9}{20}sin(2x) + \frac{3}{20}(9sin^{2}(2x) + 280cos(2x) + 280)^{\frac{1}{2}}\right)}{dx}\\=&\frac{9}{20}cos(2x)*2 + \frac{3}{20}(\frac{\frac{1}{2}(9*2sin(2x)cos(2x)*2 + 280*-sin(2x)*2 + 0)}{(9sin^{2}(2x) + 280cos(2x) + 280)^{\frac{1}{2}}})\\=&\frac{9cos(2x)}{10} + \frac{27sin(2x)cos(2x)}{10(9sin^{2}(2x) + 280cos(2x) + 280)^{\frac{1}{2}}} - \frac{42sin(2x)}{(9sin^{2}(2x) + 280cos(2x) + 280)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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