There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {(sin(3)x)}^{2} + {cos(x)}^{4} + \frac{cot(x)}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}sin^{2}(3) + cos^{4}(x) + \frac{1}{2}cot(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{2}sin^{2}(3) + cos^{4}(x) + \frac{1}{2}cot(x)\right)}{dx}\\=&2xsin^{2}(3) + x^{2}*2sin(3)cos(3)*0 + -4cos^{3}(x)sin(x) + \frac{1}{2}*-csc^{2}(x)\\=&2xsin^{2}(3) - 4sin(x)cos^{3}(x) - \frac{csc^{2}(x)}{2}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2xsin^{2}(3) - 4sin(x)cos^{3}(x) - \frac{csc^{2}(x)}{2}\right)}{dx}\\=&2sin^{2}(3) + 2x*2sin(3)cos(3)*0 - 4cos(x)cos^{3}(x) - 4sin(x)*-3cos^{2}(x)sin(x) - \frac{-2csc^{2}(x)cot(x)}{2}\\=&12sin^{2}(x)cos^{2}(x) - 4cos^{4}(x) + 2sin^{2}(3) + cot(x)csc^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 12sin^{2}(x)cos^{2}(x) - 4cos^{4}(x) + 2sin^{2}(3) + cot(x)csc^{2}(x)\right)}{dx}\\=&12*2sin(x)cos(x)cos^{2}(x) + 12sin^{2}(x)*-2cos(x)sin(x) - 4*-4cos^{3}(x)sin(x) + 2*2sin(3)cos(3)*0 + -csc^{2}(x)csc^{2}(x) + cot(x)*-2csc^{2}(x)cot(x)\\=&40sin(x)cos^{3}(x) - 24sin^{3}(x)cos(x) - csc^{4}(x) - 2cot^{2}(x)csc^{2}(x)\\ \end{split}\end{equation} \]

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