There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({e}^{(48.157543 - \frac{5622.7}{x} - 4.70504ln(x))})}{1000}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 0.001{e}^{(\frac{-5622.7}{x} - 4.70504ln(x) + 48.157543)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 0.001{e}^{(\frac{-5622.7}{x} - 4.70504ln(x) + 48.157543)}\right)}{dx}\\=&0.001({e}^{(\frac{-5622.7}{x} - 4.70504ln(x) + 48.157543)}((\frac{-5622.7*-1}{x^{2}} - \frac{4.70504}{(x)} + 0)ln(e) + \frac{(\frac{-5622.7}{x} - 4.70504ln(x) + 48.157543)(0)}{(e)}))\\=&\frac{5.6227{e}^{(\frac{-5622.7}{x} - 4.70504ln(x) + 48.157543)}}{x^{2}} - \frac{0.00470504{e}^{(\frac{-5622.7}{x} - 4.70504ln(x) + 48.157543)}}{x}\\ \end{split}\end{equation} \]

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