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

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