There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 30cos(x) + {(2500 - 900{(sin(x))}^{2})}^{\frac{1}{2}} - 40\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 30cos(x) + (-900sin^{2}(x) + 2500)^{\frac{1}{2}} - 40\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 30cos(x) + (-900sin^{2}(x) + 2500)^{\frac{1}{2}} - 40\right)}{dx}\\=&30*-sin(x) + (\frac{\frac{1}{2}(-900*2sin(x)cos(x) + 0)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}}) + 0\\=&-30sin(x) - \frac{900sin(x)cos(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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