There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{-1800sin(x)cos(x)}{(2{(2500 - 900({sin(x)}^{2}))}^{\frac{1}{2}})}) - 30sin(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-900sin(x)cos(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} - 30sin(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-900sin(x)cos(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} - 30sin(x)\right)}{dx}\\=&-900(\frac{\frac{-1}{2}(-900*2sin(x)cos(x) + 0)}{(-900sin^{2}(x) + 2500)^{\frac{3}{2}}})sin(x)cos(x) - \frac{900cos(x)cos(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} - \frac{900sin(x)*-sin(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} - 30cos(x)\\=&\frac{-810000sin^{2}(x)cos^{2}(x)}{(-900sin^{2}(x) + 2500)^{\frac{3}{2}}} - \frac{900cos^{2}(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} + \frac{900sin^{2}(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} - 30cos(x)\\ \end{split}\end{equation} \]

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