There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 12sin(x) - 12cos(x) + xcos(x) + xsin(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 12sin(x) - 12cos(x) + xcos(x) + xsin(x)\right)}{dx}\\=&12cos(x) - 12*-sin(x) + cos(x) + x*-sin(x) + sin(x) + xcos(x)\\=&13cos(x) + 13sin(x) - xsin(x) + xcos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 13cos(x) + 13sin(x) - xsin(x) + xcos(x)\right)}{dx}\\=&13*-sin(x) + 13cos(x) - sin(x) - xcos(x) + cos(x) + x*-sin(x)\\=&-14sin(x) + 14cos(x) - xcos(x) - xsin(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -14sin(x) + 14cos(x) - xcos(x) - xsin(x)\right)}{dx}\\=&-14cos(x) + 14*-sin(x) - cos(x) - x*-sin(x) - sin(x) - xcos(x)\\=&-15cos(x) - 15sin(x) + xsin(x) - xcos(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -15cos(x) - 15sin(x) + xsin(x) - xcos(x)\right)}{dx}\\=&-15*-sin(x) - 15cos(x) + sin(x) + xcos(x) - cos(x) - x*-sin(x)\\=&16sin(x) - 16cos(x) + xcos(x) + xsin(x)\\ \end{split}\end{equation} \]

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