There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({t}^{2} + t - 24)({t}^{-3} - {t}^{3} - 7t)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{t} - t^{5} + 17t^{3} + \frac{1}{t^{2}} - t^{4} - 7t^{2} - \frac{24}{t^{3}} + 168t\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{t} - t^{5} + 17t^{3} + \frac{1}{t^{2}} - t^{4} - 7t^{2} - \frac{24}{t^{3}} + 168t\right)}{dx}\\=&0 + 0 + 0 + 0 + 0 + 0 + 0 + 0\\=&0\\ \end{split}\end{equation} \]

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