There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 500(1 + x) - 1000(1 + X)(1 + 2x){\frac{1}{x}}^{2} - 2x(1 + x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{2000}{x} - 2x^{2} - \frac{1000}{x^{2}} - \frac{2000X}{x} - \frac{1000X}{x^{2}} + 498x + 500\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{2000}{x} - 2x^{2} - \frac{1000}{x^{2}} - \frac{2000X}{x} - \frac{1000X}{x^{2}} + 498x + 500\right)}{dx}\\=& - \frac{2000*-1}{x^{2}} - 2*2x - \frac{1000*-2}{x^{3}} - \frac{2000X*-1}{x^{2}} - \frac{1000X*-2}{x^{3}} + 498 + 0\\=&\frac{2000}{x^{2}} - 4x + \frac{2000}{x^{3}} + \frac{2000X}{x^{2}} + \frac{2000X}{x^{3}} + 498\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！