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

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