There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ({x}^{2}){(sin(x))}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}sin^{2}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{2}sin^{2}(x)\right)}{dx}\\=&2xsin^{2}(x) + x^{2}*2sin(x)cos(x)\\=&2x^{2}sin(x)cos(x) + 2xsin^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2x^{2}sin(x)cos(x) + 2xsin^{2}(x)\right)}{dx}\\=&2*2xsin(x)cos(x) + 2x^{2}cos(x)cos(x) + 2x^{2}sin(x)*-sin(x) + 2sin^{2}(x) + 2x*2sin(x)cos(x)\\=&8xsin(x)cos(x) + 2x^{2}cos^{2}(x) - 2x^{2}sin^{2}(x) + 2sin^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 8xsin(x)cos(x) + 2x^{2}cos^{2}(x) - 2x^{2}sin^{2}(x) + 2sin^{2}(x)\right)}{dx}\\=&8sin(x)cos(x) + 8xcos(x)cos(x) + 8xsin(x)*-sin(x) + 2*2xcos^{2}(x) + 2x^{2}*-2cos(x)sin(x) - 2*2xsin^{2}(x) - 2x^{2}*2sin(x)cos(x) + 2*2sin(x)cos(x)\\=&12sin(x)cos(x) + 12xcos^{2}(x) - 8x^{2}sin(x)cos(x) - 12xsin^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 12sin(x)cos(x) + 12xcos^{2}(x) - 8x^{2}sin(x)cos(x) - 12xsin^{2}(x)\right)}{dx}\\=&12cos(x)cos(x) + 12sin(x)*-sin(x) + 12cos^{2}(x) + 12x*-2cos(x)sin(x) - 8*2xsin(x)cos(x) - 8x^{2}cos(x)cos(x) - 8x^{2}sin(x)*-sin(x) - 12sin^{2}(x) - 12x*2sin(x)cos(x)\\=&24cos^{2}(x) - 24sin^{2}(x) - 64xsin(x)cos(x) - 8x^{2}cos^{2}(x) + 8x^{2}sin^{2}(x)\\ \end{split}\end{equation} \]

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