There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 100x((2{\frac{1}{e}}^{x} + 10) - 1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 200x{\frac{1}{e}}^{x} + 900x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 200x{\frac{1}{e}}^{x} + 900x\right)}{dx}\\=&200{\frac{1}{e}}^{x} + 200x({\frac{1}{e}}^{x}((1)ln(\frac{1}{e}) + \frac{(x)(\frac{-0}{e^{2}})}{(\frac{1}{e})})) + 900\\=&200{\frac{1}{e}}^{x} - 200x{\frac{1}{e}}^{x} + 900\\ \end{split}\end{equation} \]

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