There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 1000(\frac{((x + 15)*0.0045 + 1.05)}{(x*0.0045 + 1.05)} - 1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{4.5x}{(0.0045x + 1.05)} + \frac{67.5}{(0.0045x + 1.05)} + \frac{1050}{(0.0045x + 1.05)} - 1000\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{4.5x}{(0.0045x + 1.05)} + \frac{67.5}{(0.0045x + 1.05)} + \frac{1050}{(0.0045x + 1.05)} - 1000\right)}{dx}\\=&4.5(\frac{-(0.0045 + 0)}{(0.0045x + 1.05)^{2}})x + \frac{4.5}{(0.0045x + 1.05)} + 67.5(\frac{-(0.0045 + 0)}{(0.0045x + 1.05)^{2}}) + 1050(\frac{-(0.0045 + 0)}{(0.0045x + 1.05)^{2}}) + 0\\=&\frac{-0.02025x}{(0.0045x + 1.05)(0.0045x + 1.05)} - \frac{0.30375}{(0.0045x + 1.05)(0.0045x + 1.05)} - \frac{4.725}{(0.0045x + 1.05)(0.0045x + 1.05)} + \frac{4.5}{(0.0045x + 1.05)}\\ \end{split}\end{equation} \]

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