There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(\frac{sin(sqrt(x))}{(cos(\frac{2}{x}) - cos(1 + x + (2 + 3)))})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{sin(sqrt(x))}{(cos(\frac{2}{x}) - cos(x + 6))})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{sin(sqrt(x))}{(cos(\frac{2}{x}) - cos(x + 6))})\right)}{dx}\\=&\frac{((\frac{-(\frac{-sin(\frac{2}{x})*2*-1}{x^{2}} - -sin(x + 6)(1 + 0))}{(cos(\frac{2}{x}) - cos(x + 6))^{2}})sin(sqrt(x)) + \frac{cos(sqrt(x))*\frac{1}{2}}{(cos(\frac{2}{x}) - cos(x + 6))(x)^{\frac{1}{2}}})*\frac{1}{2}}{(\frac{sin(sqrt(x))}{(cos(\frac{2}{x}) - cos(x + 6))})^{\frac{1}{2}}}\\=&\frac{-sin(\frac{2}{x})sin^{\frac{1}{2}}(sqrt(x))}{(cos(\frac{2}{x}) - cos(x + 6))^{\frac{3}{2}}x^{2}} - \frac{sin(x + 6)sin^{\frac{1}{2}}(sqrt(x))}{2(cos(\frac{2}{x}) - cos(x + 6))^{\frac{3}{2}}} + \frac{cos(sqrt(x))}{4(cos(\frac{2}{x}) - cos(x + 6))^{\frac{1}{2}}x^{\frac{1}{2}}sin^{\frac{1}{2}}(sqrt(x))}\\ \end{split}\end{equation} \]

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