There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 0.5{x}^{2}{(sin(x))}^{2} + 0.5{x}^{2}cos(2x) - 0.5xsin(2x) - 0.25cos(2)x\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 0.5x^{2}sin(x)sin(x) + 0.5x^{2}cos(2x) - 0.5xsin(2x) - 0.25xcos(2)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 0.5x^{2}sin(x)sin(x) + 0.5x^{2}cos(2x) - 0.5xsin(2x) - 0.25xcos(2)\right)}{dx}\\=&0.5*2xsin(x)sin(x) + 0.5x^{2}cos(x)sin(x) + 0.5x^{2}sin(x)cos(x) + 0.5*2xcos(2x) + 0.5x^{2}*-sin(2x)*2 - 0.5sin(2x) - 0.5xcos(2x)*2 - 0.25cos(2) - 0.25x*-sin(2)*0\\=&xsin(x)sin(x) + 0.5x^{2}sin(x)cos(x) + 0.5x^{2}sin(x)cos(x) + xcos(2x) - x^{2}sin(2x) - 0.5sin(2x) - xcos(2x) - 0.25cos(2)\\ \end{split}\end{equation} \]

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