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

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