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

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