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

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