There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 4sin(x) - 4cos(x) + xcos(x) + xsin(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 4sin(x) - 4cos(x) + xcos(x) + xsin(x)\right)}{dx}\\=&4cos(x) - 4*-sin(x) + cos(x) + x*-sin(x) + sin(x) + xcos(x)\\=&5cos(x) + 5sin(x) - xsin(x) + xcos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 5cos(x) + 5sin(x) - xsin(x) + xcos(x)\right)}{dx}\\=&5*-sin(x) + 5cos(x) - sin(x) - xcos(x) + cos(x) + x*-sin(x)\\=&-6sin(x) + 6cos(x) - xcos(x) - xsin(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -6sin(x) + 6cos(x) - xcos(x) - xsin(x)\right)}{dx}\\=&-6cos(x) + 6*-sin(x) - cos(x) - x*-sin(x) - sin(x) - xcos(x)\\=&-7cos(x) - 7sin(x) + xsin(x) - xcos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -7cos(x) - 7sin(x) + xsin(x) - xcos(x)\right)}{dx}\\=&-7*-sin(x) - 7cos(x) + sin(x) + xcos(x) - cos(x) - x*-sin(x)\\=&8sin(x) - 8cos(x) + xcos(x) + xsin(x)\\ \end{split}\end{equation} \]

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