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

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