There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ -8sin(x)cos(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -8sin(x)cos(x)\right)}{dx}\\=&-8cos(x)cos(x) - 8sin(x)*-sin(x)\\=&-8cos^{2}(x) + 8sin^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -8cos^{2}(x) + 8sin^{2}(x)\right)}{dx}\\=&-8*-2cos(x)sin(x) + 8*2sin(x)cos(x)\\=&32sin(x)cos(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 32sin(x)cos(x)\right)}{dx}\\=&32cos(x)cos(x) + 32sin(x)*-sin(x)\\=&32cos^{2}(x) - 32sin^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 32cos^{2}(x) - 32sin^{2}(x)\right)}{dx}\\=&32*-2cos(x)sin(x) - 32*2sin(x)cos(x)\\=&-128sin(x)cos(x)\\ \end{split}\end{equation} \]

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