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

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