There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ x*3sin(x)cos(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 3xsin(x)cos(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 3xsin(x)cos(x)\right)}{dx}\\=&3sin(x)cos(x) + 3xcos(x)cos(x) + 3xsin(x)*-sin(x)\\=&3sin(x)cos(x) + 3xcos^{2}(x) - 3xsin^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3sin(x)cos(x) + 3xcos^{2}(x) - 3xsin^{2}(x)\right)}{dx}\\=&3cos(x)cos(x) + 3sin(x)*-sin(x) + 3cos^{2}(x) + 3x*-2cos(x)sin(x) - 3sin^{2}(x) - 3x*2sin(x)cos(x)\\=&6cos^{2}(x) - 6sin^{2}(x) - 12xsin(x)cos(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 6cos^{2}(x) - 6sin^{2}(x) - 12xsin(x)cos(x)\right)}{dx}\\=&6*-2cos(x)sin(x) - 6*2sin(x)cos(x) - 12sin(x)cos(x) - 12xcos(x)cos(x) - 12xsin(x)*-sin(x)\\=&-36sin(x)cos(x) - 12xcos^{2}(x) + 12xsin^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -36sin(x)cos(x) - 12xcos^{2}(x) + 12xsin^{2}(x)\right)}{dx}\\=&-36cos(x)cos(x) - 36sin(x)*-sin(x) - 12cos^{2}(x) - 12x*-2cos(x)sin(x) + 12sin^{2}(x) + 12x*2sin(x)cos(x)\\=&-48cos^{2}(x) + 48sin^{2}(x) + 48xsin(x)cos(x)\\ \end{split}\end{equation} \]

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