There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ -8({x}^{3})cos({x}^{2}) - 12xsin({x}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -8x^{3}cos(x^{2}) - 12xsin(x^{2})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -8x^{3}cos(x^{2}) - 12xsin(x^{2})\right)}{dx}\\=&-8*3x^{2}cos(x^{2}) - 8x^{3}*-sin(x^{2})*2x - 12sin(x^{2}) - 12xcos(x^{2})*2x\\=&-48x^{2}cos(x^{2}) + 16x^{4}sin(x^{2}) - 12sin(x^{2})\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -48x^{2}cos(x^{2}) + 16x^{4}sin(x^{2}) - 12sin(x^{2})\right)}{dx}\\=&-48*2xcos(x^{2}) - 48x^{2}*-sin(x^{2})*2x + 16*4x^{3}sin(x^{2}) + 16x^{4}cos(x^{2})*2x - 12cos(x^{2})*2x\\=&-120xcos(x^{2}) + 160x^{3}sin(x^{2}) + 32x^{5}cos(x^{2})\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -120xcos(x^{2}) + 160x^{3}sin(x^{2}) + 32x^{5}cos(x^{2})\right)}{dx}\\=&-120cos(x^{2}) - 120x*-sin(x^{2})*2x + 160*3x^{2}sin(x^{2}) + 160x^{3}cos(x^{2})*2x + 32*5x^{4}cos(x^{2}) + 32x^{5}*-sin(x^{2})*2x\\=&-120cos(x^{2}) + 720x^{2}sin(x^{2}) + 480x^{4}cos(x^{2}) - 64x^{6}sin(x^{2})\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -120cos(x^{2}) + 720x^{2}sin(x^{2}) + 480x^{4}cos(x^{2}) - 64x^{6}sin(x^{2})\right)}{dx}\\=&-120*-sin(x^{2})*2x + 720*2xsin(x^{2}) + 720x^{2}cos(x^{2})*2x + 480*4x^{3}cos(x^{2}) + 480x^{4}*-sin(x^{2})*2x - 64*6x^{5}sin(x^{2}) - 64x^{6}cos(x^{2})*2x\\=&1680xsin(x^{2}) + 3360x^{3}cos(x^{2}) - 1344x^{5}sin(x^{2}) - 128x^{7}cos(x^{2})\\ \end{split}\end{equation} \]

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