There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{400(7.5 - rt)}{(1 + 399{e}^{(-0.02806(174.28 + t))})} - (500 + 7.1t)\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{400rt}{(399{e}^{(-0.02806t - 4.8902968)} + 1)} + \frac{3000}{(399{e}^{(-0.02806t - 4.8902968)} + 1)} - 7.1t - 500\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{400rt}{(399{e}^{(-0.02806t - 4.8902968)} + 1)} + \frac{3000}{(399{e}^{(-0.02806t - 4.8902968)} + 1)} - 7.1t - 500\right)}{dt}\\=& - 400(\frac{-(399({e}^{(-0.02806t - 4.8902968)}((-0.02806 + 0)ln(e) + \frac{(-0.02806t - 4.8902968)(0)}{(e)})) + 0)}{(399{e}^{(-0.02806t - 4.8902968)} + 1)^{2}})rt - \frac{400r}{(399{e}^{(-0.02806t - 4.8902968)} + 1)} + 3000(\frac{-(399({e}^{(-0.02806t - 4.8902968)}((-0.02806 + 0)ln(e) + \frac{(-0.02806t - 4.8902968)(0)}{(e)})) + 0)}{(399{e}^{(-0.02806t - 4.8902968)} + 1)^{2}}) - 7.1 + 0\\=& - \frac{4478.376rt{e}^{(-0.02806t - 4.8902968)}}{(399{e}^{(-0.02806t - 4.8902968)} + 1)(399{e}^{(-0.02806t - 4.8902968)} + 1)} - \frac{400r}{(399{e}^{(-0.02806t - 4.8902968)} + 1)} + \frac{33587.82{e}^{(-0.02806t - 4.8902968)}}{(399{e}^{(-0.02806t - 4.8902968)} + 1)(399{e}^{(-0.02806t - 4.8902968)} + 1)} - 7.1\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！