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

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