There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{15000}{(1 + {2.71828182845905}^{(\frac{-(x - 7500)}{1500})})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{15000}{({2.71828182845905}^{(-0.0006666666667x + 5)} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{15000}{({2.71828182845905}^{(-0.0006666666667x + 5)} + 1)}\right)}{dx}\\=&15000(\frac{-(({2.71828182845905}^{(-0.0006666666667x + 5)}((-0.0006666666667 + 0)ln(2.71828182845905) + \frac{(-0.0006666666667x + 5)(0)}{(2.71828182845905)})) + 0)}{({2.71828182845905}^{(-0.0006666666667x + 5)} + 1)^{2}})\\=&\frac{10 * {2.71828182845905}^{(-0.0006666666667x + 5)}ln(2.71828182845905)}{({2.71828182845905}^{(-0.0006666666667x + 5)} + 1)({2.71828182845905}^{(-0.0006666666667x + 5)} + 1)}\\ \end{split}\end{equation} \]

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