There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (1 - cos(x))(x - sin(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - xcos(x) + sin(x)cos(x) + x - sin(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - xcos(x) + sin(x)cos(x) + x - sin(x)\right)}{dx}\\=& - cos(x) - x*-sin(x) + cos(x)cos(x) + sin(x)*-sin(x) + 1 - cos(x)\\=& - 2cos(x) + xsin(x) + cos^{2}(x) - sin^{2}(x) + 1\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - 2cos(x) + xsin(x) + cos^{2}(x) - sin^{2}(x) + 1\right)}{dx}\\=& - 2*-sin(x) + sin(x) + xcos(x) + -2cos(x)sin(x) - 2sin(x)cos(x) + 0\\=& - 4sin(x)cos(x) + 3sin(x) + xcos(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 4sin(x)cos(x) + 3sin(x) + xcos(x)\right)}{dx}\\=& - 4cos(x)cos(x) - 4sin(x)*-sin(x) + 3cos(x) + cos(x) + x*-sin(x)\\=& - 4cos^{2}(x) + 4sin^{2}(x) + 4cos(x) - xsin(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - 4cos^{2}(x) + 4sin^{2}(x) + 4cos(x) - xsin(x)\right)}{dx}\\=& - 4*-2cos(x)sin(x) + 4*2sin(x)cos(x) + 4*-sin(x) - sin(x) - xcos(x)\\=&16sin(x)cos(x) - 5sin(x) - xcos(x)\\ \end{split}\end{equation} \]

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