There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {x}^{5}{\frac{1}{(x + 1500)}}^{7}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{5}}{(x + 1500)^{7}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{5}}{(x + 1500)^{7}}\right)}{dx}\\=&(\frac{-7(1 + 0)}{(x + 1500)^{8}})x^{5} + \frac{5x^{4}}{(x + 1500)^{7}}\\=&\frac{-7x^{5}}{(x + 1500)^{8}} + \frac{5x^{4}}{(x + 1500)^{7}}\\ \end{split}\end{equation} \]

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