There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sin(x)cos(x) - sin(cos(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(x)cos(x) - sin(cos(x))\right)}{dx}\\=&cos(x)cos(x) + sin(x)*-sin(x) - cos(cos(x))*-sin(x)\\=&cos^{2}(x) + sin(x)cos(cos(x)) - sin^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( cos^{2}(x) + sin(x)cos(cos(x)) - sin^{2}(x)\right)}{dx}\\=&-2cos(x)sin(x) + cos(x)cos(cos(x)) + sin(x)*-sin(cos(x))*-sin(x) - 2sin(x)cos(x)\\=&-4sin(x)cos(x) + cos(x)cos(cos(x)) + sin(cos(x))sin^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -4sin(x)cos(x) + cos(x)cos(cos(x)) + sin(cos(x))sin^{2}(x)\right)}{dx}\\=&-4cos(x)cos(x) - 4sin(x)*-sin(x) + -sin(x)cos(cos(x)) + cos(x)*-sin(cos(x))*-sin(x) + cos(cos(x))*-sin(x)sin^{2}(x) + sin(cos(x))*2sin(x)cos(x)\\=&-4cos^{2}(x) + 3sin(x)sin(cos(x))cos(x) - sin(x)cos(cos(x)) - sin^{3}(x)cos(cos(x)) + 4sin^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -4cos^{2}(x) + 3sin(x)sin(cos(x))cos(x) - sin(x)cos(cos(x)) - sin^{3}(x)cos(cos(x)) + 4sin^{2}(x)\right)}{dx}\\=&-4*-2cos(x)sin(x) + 3cos(x)sin(cos(x))cos(x) + 3sin(x)cos(cos(x))*-sin(x)cos(x) + 3sin(x)sin(cos(x))*-sin(x) - cos(x)cos(cos(x)) - sin(x)*-sin(cos(x))*-sin(x) - 3sin^{2}(x)cos(x)cos(cos(x)) - sin^{3}(x)*-sin(cos(x))*-sin(x) + 4*2sin(x)cos(x)\\=& - 3sin^{2}(x)cos(x)cos(cos(x)) - 3sin^{2}(x)cos(cos(x))cos(x) + 3sin(cos(x))cos^{2}(x) - 3sin^{2}(x)sin(cos(x)) - cos(x)cos(cos(x)) - sin(cos(x))sin^{2}(x) + 16sin(x)cos(x) - sin(cos(x))sin^{4}(x)\\ \end{split}\end{equation} \]

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