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

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