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

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