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

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