There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {v}^{2}t{\frac{1}{({v}^{2}{t}^{2} + {a}^{2})}}^{\frac{1}{2}}\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{v^{2}t}{(v^{2}t^{2} + a^{2})^{\frac{1}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{v^{2}t}{(v^{2}t^{2} + a^{2})^{\frac{1}{2}}}\right)}{dt}\\=&(\frac{\frac{-1}{2}(v^{2}*2t + 0)}{(v^{2}t^{2} + a^{2})^{\frac{3}{2}}})v^{2}t + \frac{v^{2}}{(v^{2}t^{2} + a^{2})^{\frac{1}{2}}}\\=&\frac{-v^{4}t^{2}}{(v^{2}t^{2} + a^{2})^{\frac{3}{2}}} + \frac{v^{2}}{(v^{2}t^{2} + a^{2})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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