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

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