There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (x*2){(sin(x))}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2xsin^{2}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2xsin^{2}(x)\right)}{dx}\\=&2sin^{2}(x) + 2x*2sin(x)cos(x)\\=&2sin^{2}(x) + 4xsin(x)cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2sin^{2}(x) + 4xsin(x)cos(x)\right)}{dx}\\=&2*2sin(x)cos(x) + 4sin(x)cos(x) + 4xcos(x)cos(x) + 4xsin(x)*-sin(x)\\=&8sin(x)cos(x) + 4xcos^{2}(x) - 4xsin^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 8sin(x)cos(x) + 4xcos^{2}(x) - 4xsin^{2}(x)\right)}{dx}\\=&8cos(x)cos(x) + 8sin(x)*-sin(x) + 4cos^{2}(x) + 4x*-2cos(x)sin(x) - 4sin^{2}(x) - 4x*2sin(x)cos(x)\\=&12cos^{2}(x) - 12sin^{2}(x) - 16xsin(x)cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 12cos^{2}(x) - 12sin^{2}(x) - 16xsin(x)cos(x)\right)}{dx}\\=&12*-2cos(x)sin(x) - 12*2sin(x)cos(x) - 16sin(x)cos(x) - 16xcos(x)cos(x) - 16xsin(x)*-sin(x)\\=&-64sin(x)cos(x) - 16xcos^{2}(x) + 16xsin^{2}(x)\\ \end{split}\end{equation} \]

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