There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ 2{x}^{3}{(cos(x))}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2x^{3}cos^{2}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2x^{3}cos^{2}(x)\right)}{dx}\\=&2*3x^{2}cos^{2}(x) + 2x^{3}*-2cos(x)sin(x)\\=&6x^{2}cos^{2}(x) - 4x^{3}sin(x)cos(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 6x^{2}cos^{2}(x) - 4x^{3}sin(x)cos(x)\right)}{dx}\\=&6*2xcos^{2}(x) + 6x^{2}*-2cos(x)sin(x) - 4*3x^{2}sin(x)cos(x) - 4x^{3}cos(x)cos(x) - 4x^{3}sin(x)*-sin(x)\\=& - 4x^{3}cos^{2}(x) - 24x^{2}sin(x)cos(x) + 12xcos^{2}(x) + 4x^{3}sin^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( - 4x^{3}cos^{2}(x) - 24x^{2}sin(x)cos(x) + 12xcos^{2}(x) + 4x^{3}sin^{2}(x)\right)}{dx}\\=& - 4*3x^{2}cos^{2}(x) - 4x^{3}*-2cos(x)sin(x) - 24*2xsin(x)cos(x) - 24x^{2}cos(x)cos(x) - 24x^{2}sin(x)*-sin(x) + 12cos^{2}(x) + 12x*-2cos(x)sin(x) + 4*3x^{2}sin^{2}(x) + 4x^{3}*2sin(x)cos(x)\\=& - 36x^{2}cos^{2}(x) + 16x^{3}sin(x)cos(x) - 72xsin(x)cos(x) + 36x^{2}sin^{2}(x) + 12cos^{2}(x)\\ \end{split}\end{equation} \]

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