There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(1 + {x}^{2})}^{5}{(1 - 2{x}^{2})}^{8}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (-2x^{2} + 1)^{8}x^{10} + 5(-2x^{2} + 1)^{8}x^{8} + 10(-2x^{2} + 1)^{8}x^{6} + 10(-2x^{2} + 1)^{8}x^{4} + 5(-2x^{2} + 1)^{8}x^{2} + (-2x^{2} + 1)^{8}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (-2x^{2} + 1)^{8}x^{10} + 5(-2x^{2} + 1)^{8}x^{8} + 10(-2x^{2} + 1)^{8}x^{6} + 10(-2x^{2} + 1)^{8}x^{4} + 5(-2x^{2} + 1)^{8}x^{2} + (-2x^{2} + 1)^{8}\right)}{dx}\\=&(8(-2x^{2} + 1)^{7}(-2*2x + 0))x^{10} + (-2x^{2} + 1)^{8}*10x^{9} + 5(8(-2x^{2} + 1)^{7}(-2*2x + 0))x^{8} + 5(-2x^{2} + 1)^{8}*8x^{7} + 10(8(-2x^{2} + 1)^{7}(-2*2x + 0))x^{6} + 10(-2x^{2} + 1)^{8}*6x^{5} + 10(8(-2x^{2} + 1)^{7}(-2*2x + 0))x^{4} + 10(-2x^{2} + 1)^{8}*4x^{3} + 5(8(-2x^{2} + 1)^{7}(-2*2x + 0))x^{2} + 5(-2x^{2} + 1)^{8}*2x + (8(-2x^{2} + 1)^{7}(-2*2x + 0))\\=&-32(-2x^{2} + 1)^{7}x^{11} + 10(-2x^{2} + 1)^{8}x^{9} - 160(-2x^{2} + 1)^{7}x^{9} + 40(-2x^{2} + 1)^{8}x^{7} - 320(-2x^{2} + 1)^{7}x^{7} + 60(-2x^{2} + 1)^{8}x^{5} - 320(-2x^{2} + 1)^{7}x^{5} + 40(-2x^{2} + 1)^{8}x^{3} - 160(-2x^{2} + 1)^{7}x^{3} + 10(-2x^{2} + 1)^{8}x - 32(-2x^{2} + 1)^{7}x\\ \end{split}\end{equation} \]

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