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

Your problem has not been solved here? Please take a look at the  hot problems ！