There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(x + 1){({x}^{2} - 5x - \frac{6}{x} - 8)}^{1}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x^{3} - 2x^{2} - \frac{13}{2}x - \frac{3}{x} - 7\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x^{3} - 2x^{2} - \frac{13}{2}x - \frac{3}{x} - 7\right)}{dx}\\=&\frac{1}{2}*3x^{2} - 2*2x - \frac{13}{2} - \frac{3*-1}{x^{2}} + 0\\=&\frac{3x^{2}}{2} - 4x + \frac{3}{x^{2}} - \frac{13}{2}\\ \end{split}\end{equation} \]

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