There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {e}^{((t) + (\frac{1}{2})*5{t}^{2})}\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{(t + \frac{5}{2}t^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{(t + \frac{5}{2}t^{2})}\right)}{dt}\\=&({e}^{(t + \frac{5}{2}t^{2})}((1 + \frac{5}{2}*2t)ln(e) + \frac{(t + \frac{5}{2}t^{2})(0)}{(e)}))\\=&5t{e}^{(t + \frac{5}{2}t^{2})} + {e}^{(t + \frac{5}{2}t^{2})}\\ \end{split}\end{equation} \]

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