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

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