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

Your problem has not been solved here? Please take a look at the  hot problems ！