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

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