There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(3600 + {(\frac{(6 - 3(cos(x)))*20}{sin(x)})}^{2})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (\frac{3600cos^{2}(x)}{sin^{2}(x)} - \frac{14400cos(x)}{sin^{2}(x)} + \frac{14400}{sin^{2}(x)} + 3600)^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (\frac{3600cos^{2}(x)}{sin^{2}(x)} - \frac{14400cos(x)}{sin^{2}(x)} + \frac{14400}{sin^{2}(x)} + 3600)^{\frac{1}{2}}\right)}{dx}\\=&(\frac{\frac{1}{2}(\frac{3600*-2cos(x)cos^{2}(x)}{sin^{3}(x)} + \frac{3600*-2cos(x)sin(x)}{sin^{2}(x)} - \frac{14400*-2cos(x)cos(x)}{sin^{3}(x)} - \frac{14400*-sin(x)}{sin^{2}(x)} + \frac{14400*-2cos(x)}{sin^{3}(x)} + 0)}{(\frac{3600cos^{2}(x)}{sin^{2}(x)} - \frac{14400cos(x)}{sin^{2}(x)} + \frac{14400}{sin^{2}(x)} + 3600)^{\frac{1}{2}}})\\=&\frac{-3600cos^{3}(x)}{(\frac{3600cos^{2}(x)}{sin^{2}(x)} - \frac{14400cos(x)}{sin^{2}(x)} + \frac{14400}{sin^{2}(x)} + 3600)^{\frac{1}{2}}sin^{3}(x)} - \frac{3600cos(x)}{(\frac{3600cos^{2}(x)}{sin^{2}(x)} - \frac{14400cos(x)}{sin^{2}(x)} + \frac{14400}{sin^{2}(x)} + 3600)^{\frac{1}{2}}sin(x)} + \frac{14400cos^{2}(x)}{(\frac{3600cos^{2}(x)}{sin^{2}(x)} - \frac{14400cos(x)}{sin^{2}(x)} + \frac{14400}{sin^{2}(x)} + 3600)^{\frac{1}{2}}sin^{3}(x)} - \frac{14400cos(x)}{(\frac{3600cos^{2}(x)}{sin^{2}(x)} - \frac{14400cos(x)}{sin^{2}(x)} + \frac{14400}{sin^{2}(x)} + 3600)^{\frac{1}{2}}sin^{3}(x)} + \frac{7200}{(\frac{3600cos^{2}(x)}{sin^{2}(x)} - \frac{14400cos(x)}{sin^{2}(x)} + \frac{14400}{sin^{2}(x)} + 3600)^{\frac{1}{2}}sin(x)}\\ \end{split}\end{equation} \]

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