There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ -2(1 - cos(x))sin(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2sin(x)cos(x) - 2sin(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2sin(x)cos(x) - 2sin(x)\right)}{dx}\\=&2cos(x)cos(x) + 2sin(x)*-sin(x) - 2cos(x)\\=&2cos^{2}(x) - 2sin^{2}(x) - 2cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2cos^{2}(x) - 2sin^{2}(x) - 2cos(x)\right)}{dx}\\=&2*-2cos(x)sin(x) - 2*2sin(x)cos(x) - 2*-sin(x)\\=& - 8sin(x)cos(x) + 2sin(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 8sin(x)cos(x) + 2sin(x)\right)}{dx}\\=& - 8cos(x)cos(x) - 8sin(x)*-sin(x) + 2cos(x)\\=& - 8cos^{2}(x) + 8sin^{2}(x) + 2cos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - 8cos^{2}(x) + 8sin^{2}(x) + 2cos(x)\right)}{dx}\\=& - 8*-2cos(x)sin(x) + 8*2sin(x)cos(x) + 2*-sin(x)\\=&32sin(x)cos(x) - 2sin(x)\\ \end{split}\end{equation} \]

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