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

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