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

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