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

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