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

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