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

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