There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -12{sin(x)}^{2} - 48{x}^{2}{cos(x)}^{2} + 16{x}^{4}{sin(x)}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -12sin^{2}(x) - 48x^{2}cos^{2}(x) + 16x^{4}sin^{2}(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -12sin^{2}(x) - 48x^{2}cos^{2}(x) + 16x^{4}sin^{2}(x)\right)}{dx}\\=&-12*2sin(x)cos(x) - 48*2xcos^{2}(x) - 48x^{2}*-2cos(x)sin(x) + 16*4x^{3}sin^{2}(x) + 16x^{4}*2sin(x)cos(x)\\=&-24sin(x)cos(x) - 96xcos^{2}(x) + 96x^{2}sin(x)cos(x) + 32x^{4}sin(x)cos(x) + 64x^{3}sin^{2}(x)\\ \end{split}\end{equation} \]

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