There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 8({({(x + 1)}^{2} + 1)}^{2} + 1)({(x + 1)}^{3} + x + 1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 8x^{7} + 56x^{6} + 192x^{5} + 400x^{4} + 552x^{3} + 504x^{2} + 288x + 80\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 8x^{7} + 56x^{6} + 192x^{5} + 400x^{4} + 552x^{3} + 504x^{2} + 288x + 80\right)}{dx}\\=&8*7x^{6} + 56*6x^{5} + 192*5x^{4} + 400*4x^{3} + 552*3x^{2} + 504*2x + 288 + 0\\=&56x^{6} + 336x^{5} + 960x^{4} + 1600x^{3} + 1656x^{2} + 1008x + 288\\ \end{split}\end{equation} \]

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