There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{(x + 1)}^{2}}{(4{x}^{2}(1 - ln(x)))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{(-4x^{2}ln(x) + 4x^{2})} + \frac{2x}{(-4x^{2}ln(x) + 4x^{2})} + \frac{1}{(-4x^{2}ln(x) + 4x^{2})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{(-4x^{2}ln(x) + 4x^{2})} + \frac{2x}{(-4x^{2}ln(x) + 4x^{2})} + \frac{1}{(-4x^{2}ln(x) + 4x^{2})}\right)}{dx}\\=&(\frac{-(-4*2xln(x) - \frac{4x^{2}}{(x)} + 4*2x)}{(-4x^{2}ln(x) + 4x^{2})^{2}})x^{2} + \frac{2x}{(-4x^{2}ln(x) + 4x^{2})} + 2(\frac{-(-4*2xln(x) - \frac{4x^{2}}{(x)} + 4*2x)}{(-4x^{2}ln(x) + 4x^{2})^{2}})x + \frac{2}{(-4x^{2}ln(x) + 4x^{2})} + (\frac{-(-4*2xln(x) - \frac{4x^{2}}{(x)} + 4*2x)}{(-4x^{2}ln(x) + 4x^{2})^{2}})\\=&\frac{8x^{3}ln(x)}{(-4x^{2}ln(x) + 4x^{2})^{2}} + \frac{16x^{2}ln(x)}{(-4x^{2}ln(x) + 4x^{2})^{2}} + \frac{8xln(x)}{(-4x^{2}ln(x) + 4x^{2})^{2}} + \frac{2x}{(-4x^{2}ln(x) + 4x^{2})} - \frac{8x^{2}}{(-4x^{2}ln(x) + 4x^{2})^{2}} - \frac{4x^{3}}{(-4x^{2}ln(x) + 4x^{2})^{2}} - \frac{4x}{(-4x^{2}ln(x) + 4x^{2})^{2}} + \frac{2}{(-4x^{2}ln(x) + 4x^{2})}\\ \end{split}\end{equation} \]

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