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

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