There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(({x}^{5}){500}^{(5x)})}{({(k)}^{(x + 1)})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{5}{500}^{(5x)}{k}^{(-x - 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{5}{500}^{(5x)}{k}^{(-x - 1)}\right)}{dx}\\=&5x^{4}{500}^{(5x)}{k}^{(-x - 1)} + x^{5}({500}^{(5x)}((5)ln(500) + \frac{(5x)(0)}{(500)})){k}^{(-x - 1)} + x^{5}{500}^{(5x)}({k}^{(-x - 1)}((-1 + 0)ln(k) + \frac{(-x - 1)(0)}{(k)}))\\=&5x^{5}{500}^{(5x)}{k}^{(-x - 1)}ln(500) - x^{5}{k}^{(-x - 1)}{500}^{(5x)}ln(k) + 5x^{4}{500}^{(5x)}{k}^{(-x - 1)}\\ \end{split}\end{equation} \]

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