There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {({x}^{2} + 1)}^{3}{({x}^{2} + 2)}^{6}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{2} + 2)^{6}x^{6} + 3(x^{2} + 2)^{6}x^{4} + 3(x^{2} + 2)^{6}x^{2} + (x^{2} + 2)^{6}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x^{2} + 2)^{6}x^{6} + 3(x^{2} + 2)^{6}x^{4} + 3(x^{2} + 2)^{6}x^{2} + (x^{2} + 2)^{6}\right)}{dx}\\=&(6(x^{2} + 2)^{5}(2x + 0))x^{6} + (x^{2} + 2)^{6}*6x^{5} + 3(6(x^{2} + 2)^{5}(2x + 0))x^{4} + 3(x^{2} + 2)^{6}*4x^{3} + 3(6(x^{2} + 2)^{5}(2x + 0))x^{2} + 3(x^{2} + 2)^{6}*2x + (6(x^{2} + 2)^{5}(2x + 0))\\=&12x^{17} + 156x^{15} + 876x^{13} + 2772x^{11} + 5400x^{9} + 6(x^{2} + 2)^{6}x^{5} + 6624x^{7} + 12(x^{2} + 2)^{6}x^{3} + 4992x^{5} + 6(x^{2} + 2)^{6}x + 2112x^{3} + 384x\\ \end{split}\end{equation} \]

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