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

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