There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 10cos(x) - \frac{10sin(x)(10cos(x) + sqrt(100{(cos(x))}^{2} - 240 - 200sin(x)))}{10}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 10cos(x) - 10sin(x)cos(x) - sin(x)sqrt(100cos^{2}(x) - 200sin(x) - 240)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 10cos(x) - 10sin(x)cos(x) - sin(x)sqrt(100cos^{2}(x) - 200sin(x) - 240)\right)}{dx}\\=&10*-sin(x) - 10cos(x)cos(x) - 10sin(x)*-sin(x) - cos(x)sqrt(100cos^{2}(x) - 200sin(x) - 240) - \frac{sin(x)(100*-2cos(x)sin(x) - 200cos(x) + 0)*\frac{1}{2}}{(100cos^{2}(x) - 200sin(x) - 240)^{\frac{1}{2}}}\\=&10sin^{2}(x) - cos(x)sqrt(100cos^{2}(x) - 200sin(x) - 240) - 10sin(x) - 10cos^{2}(x) + \frac{100sin^{2}(x)cos(x)}{(100cos^{2}(x) - 200sin(x) - 240)^{\frac{1}{2}}} + \frac{100sin(x)cos(x)}{(100cos^{2}(x) - 200sin(x) - 240)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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