There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(2x - 2)}^{4}{({x}^{2} + x + 1)}^{5}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 16x^{14} + 16x^{13} + 16x^{12} - 64x^{11} - 64x^{10} - 64x^{9} + 96x^{8} + 96x^{7} + 96x^{6} - 64x^{5} - 64x^{4} - 64x^{3} + 16x^{2} + 16x + 16\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 16x^{14} + 16x^{13} + 16x^{12} - 64x^{11} - 64x^{10} - 64x^{9} + 96x^{8} + 96x^{7} + 96x^{6} - 64x^{5} - 64x^{4} - 64x^{3} + 16x^{2} + 16x + 16\right)}{dx}\\=&16*14x^{13} + 16*13x^{12} + 16*12x^{11} - 64*11x^{10} - 64*10x^{9} - 64*9x^{8} + 96*8x^{7} + 96*7x^{6} + 96*6x^{5} - 64*5x^{4} - 64*4x^{3} - 64*3x^{2} + 16*2x + 16 + 0\\=&224x^{13} + 208x^{12} + 192x^{11} - 704x^{10} - 640x^{9} - 576x^{8} + 768x^{7} + 672x^{6} + 576x^{5} - 320x^{4} - 256x^{3} - 192x^{2} + 32x + 16\\ \end{split}\end{equation} \]

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