There are 1 questions in this calculation: for each question, the 2 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{400(7.5 - 0.06t)}{(1 + 399e^{-4.8902968 - 0.02806t})} - 500 - 7.1t\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{24t}{(399e^{-0.02806t - 4.8902968} + 1)} + \frac{3000}{(399e^{-0.02806t - 4.8902968} + 1)} - 7.1t - 500\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{24t}{(399e^{-0.02806t - 4.8902968} + 1)} + \frac{3000}{(399e^{-0.02806t - 4.8902968} + 1)} - 7.1t - 500\right)}{dt}\\=& - 24(\frac{-(399e^{-0.02806t - 4.8902968}(-0.02806 + 0) + 0)}{(399e^{-0.02806t - 4.8902968} + 1)^{2}})t - \frac{24}{(399e^{-0.02806t - 4.8902968} + 1)} + 3000(\frac{-(399e^{-0.02806t - 4.8902968}(-0.02806 + 0) + 0)}{(399e^{-0.02806t - 4.8902968} + 1)^{2}}) - 7.1 + 0\\=& - \frac{268.70256te^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} + \frac{33587.82e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} - \frac{24}{(399e^{-0.02806t - 4.8902968} + 1)} - 7.1\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{268.70256te^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} + \frac{33587.82e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} - \frac{24}{(399e^{-0.02806t - 4.8902968} + 1)} - 7.1\right)}{dt}\\=& - \frac{268.70256(\frac{-(399e^{-0.02806t - 4.8902968}(-0.02806 + 0) + 0)}{(399e^{-0.02806t - 4.8902968} + 1)^{2}})te^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)} - \frac{268.70256(\frac{-(399e^{-0.02806t - 4.8902968}(-0.02806 + 0) + 0)}{(399e^{-0.02806t - 4.8902968} + 1)^{2}})te^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)} - \frac{268.70256e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} - \frac{268.70256te^{-0.02806t - 4.8902968}(-0.02806 + 0)}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} + \frac{33587.82(\frac{-(399e^{-0.02806t - 4.8902968}(-0.02806 + 0) + 0)}{(399e^{-0.02806t - 4.8902968} + 1)^{2}})e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)} + \frac{33587.82(\frac{-(399e^{-0.02806t - 4.8902968}(-0.02806 + 0) + 0)}{(399e^{-0.02806t - 4.8902968} + 1)^{2}})e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)} + \frac{33587.82e^{-0.02806t - 4.8902968}(-0.02806 + 0)}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} - 24(\frac{-(399e^{-0.02806t - 4.8902968}(-0.02806 + 0) + 0)}{(399e^{-0.02806t - 4.8902968} + 1)^{2}}) + 0\\=& - \frac{3008.3777396064te^{-0.02806t - 4.8902968}e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} - \frac{3008.3777396064te^{-0.02806t - 4.8902968}e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} + \frac{376047.2174508e^{-0.02806t - 4.8902968}e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} + \frac{7.5397938336te^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} + \frac{376047.2174508e^{-0.02806t - 4.8902968}e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} - \frac{268.70256e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} - \frac{942.4742292e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)} - \frac{268.70256e^{-0.02806t - 4.8902968}}{(399e^{-0.02806t - 4.8902968} + 1)(399e^{-0.02806t - 4.8902968} + 1)}\\ \end{split}\end{equation} \]

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