There are 1 questions in this calculation: for each question, the 2 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ a{e}^{(-3t)} + b{e}^{(-4t)}\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( a{e}^{(-3t)} + b{e}^{(-4t)}\right)}{dt}\\=&a({e}^{(-3t)}((-3)ln(e) + \frac{(-3t)(0)}{(e)})) + b({e}^{(-4t)}((-4)ln(e) + \frac{(-4t)(0)}{(e)}))\\=&-3a{e}^{(-3t)} - 4b{e}^{(-4t)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -3a{e}^{(-3t)} - 4b{e}^{(-4t)}\right)}{dt}\\=&-3a({e}^{(-3t)}((-3)ln(e) + \frac{(-3t)(0)}{(e)})) - 4b({e}^{(-4t)}((-4)ln(e) + \frac{(-4t)(0)}{(e)}))\\=&9a{e}^{(-3t)} + 16b{e}^{(-4t)}\\ \end{split}\end{equation} \]

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