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

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