There are 1 questions in this calculation: for each question, the 1 derivative of s is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ st{e}^{(st)} - 2{e}^{(st)}{t}^{2} - 5s{t}^{3}\ with\ respect\ to\ s：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ts{e}^{(ts)} - 2t^{2}{e}^{(ts)} - 5t^{3}s\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ts{e}^{(ts)} - 2t^{2}{e}^{(ts)} - 5t^{3}s\right)}{ds}\\=&t{e}^{(ts)} + ts({e}^{(ts)}((t)ln(e) + \frac{(ts)(0)}{(e)})) - 2t^{2}({e}^{(ts)}((t)ln(e) + \frac{(ts)(0)}{(e)})) - 5t^{3}\\=&t{e}^{(ts)} + t^{2}s{e}^{(ts)} - 2t^{3}{e}^{(ts)} - 5t^{3}\\ \end{split}\end{equation} \]

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