There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{sqrt(x({x}^{2} + 8)(8 - x))}{(x + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{sqrt(-x^{4} + 8x^{3} + 64x - 8x^{2})}{(x + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{sqrt(-x^{4} + 8x^{3} + 64x - 8x^{2})}{(x + 1)}\right)}{dx}\\=&(\frac{-(1 + 0)}{(x + 1)^{2}})sqrt(-x^{4} + 8x^{3} + 64x - 8x^{2}) + \frac{(-4x^{3} + 8*3x^{2} + 64 - 8*2x)*\frac{1}{2}}{(x + 1)(-x^{4} + 8x^{3} + 64x - 8x^{2})^{\frac{1}{2}}}\\=&\frac{-sqrt(-x^{4} + 8x^{3} + 64x - 8x^{2})}{(x + 1)^{2}} - \frac{2x^{3}}{(x + 1)(-x^{4} + 8x^{3} + 64x - 8x^{2})^{\frac{1}{2}}} + \frac{12x^{2}}{(x + 1)(-x^{4} + 8x^{3} + 64x - 8x^{2})^{\frac{1}{2}}} - \frac{8x}{(x + 1)(-x^{4} + 8x^{3} + 64x - 8x^{2})^{\frac{1}{2}}} + \frac{32}{(x + 1)(-x^{4} + 8x^{3} + 64x - 8x^{2})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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