There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(52 - 24cos(x) - 8sqrt(3)sin(x)) + sqrt(5 - 4cos(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(-24cos(x) - 8sin(x)sqrt(3) + 52) + sqrt(-4cos(x) + 5)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(-24cos(x) - 8sin(x)sqrt(3) + 52) + sqrt(-4cos(x) + 5)\right)}{dx}\\=&\frac{(-24*-sin(x) - 8cos(x)sqrt(3) - 8sin(x)*0*\frac{1}{2}*3^{\frac{1}{2}} + 0)*\frac{1}{2}}{(-24cos(x) - 8sin(x)sqrt(3) + 52)^{\frac{1}{2}}} + \frac{(-4*-sin(x) + 0)*\frac{1}{2}}{(-4cos(x) + 5)^{\frac{1}{2}}}\\=&\frac{12sin(x)}{(-24cos(x) - 8sin(x)sqrt(3) + 52)^{\frac{1}{2}}} - \frac{4cos(x)sqrt(3)}{(-24cos(x) - 8sin(x)sqrt(3) + 52)^{\frac{1}{2}}} + \frac{2sin(x)}{(-4cos(x) + 5)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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