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

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