There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(1830{t}^{9} + 183)}{({t}^{10} + t + 1)} + {e}^{(0.26t + 5)}\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1830t^{9}}{(t^{10} + t + 1)} + \frac{183}{(t^{10} + t + 1)} + {e}^{(0.26t + 5)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1830t^{9}}{(t^{10} + t + 1)} + \frac{183}{(t^{10} + t + 1)} + {e}^{(0.26t + 5)}\right)}{dt}\\=&1830(\frac{-(10t^{9} + 1 + 0)}{(t^{10} + t + 1)^{2}})t^{9} + \frac{1830*9t^{8}}{(t^{10} + t + 1)} + 183(\frac{-(10t^{9} + 1 + 0)}{(t^{10} + t + 1)^{2}}) + ({e}^{(0.26t + 5)}((0.26 + 0)ln(e) + \frac{(0.26t + 5)(0)}{(e)}))\\=&\frac{-18300t^{18}}{(t^{10} + t + 1)(t^{10} + t + 1)} - \frac{1830t^{9}}{(t^{10} + t + 1)(t^{10} + t + 1)} + \frac{16470t^{8}}{(t^{10} + t + 1)} - \frac{1830t^{9}}{(t^{10} + t + 1)(t^{10} + t + 1)} - \frac{183}{(t^{10} + t + 1)(t^{10} + t + 1)} + 0.26{e}^{(0.26t + 5)}\\ \end{split}\end{equation} \]

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