There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -2{({x}^{2} + x)}^{\frac{-1}{2}} + 2ln({x}^{\frac{1}{2}} + {(x + 1)}^{\frac{1}{2}})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-2}{(x^{2} + x)^{\frac{1}{2}}} + 2ln(x^{\frac{1}{2}} + (x + 1)^{\frac{1}{2}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-2}{(x^{2} + x)^{\frac{1}{2}}} + 2ln(x^{\frac{1}{2}} + (x + 1)^{\frac{1}{2}})\right)}{dx}\\=&-2(\frac{\frac{-1}{2}(2x + 1)}{(x^{2} + x)^{\frac{3}{2}}}) + \frac{2(\frac{\frac{1}{2}}{x^{\frac{1}{2}}} + (\frac{\frac{1}{2}(1 + 0)}{(x + 1)^{\frac{1}{2}}}))}{(x^{\frac{1}{2}} + (x + 1)^{\frac{1}{2}})}\\=&\frac{2x}{(x^{2} + x)^{\frac{3}{2}}} + \frac{1}{(x^{\frac{1}{2}} + (x + 1)^{\frac{1}{2}})x^{\frac{1}{2}}} + \frac{1}{(x + 1)^{\frac{1}{2}}(x^{\frac{1}{2}} + (x + 1)^{\frac{1}{2}})} + \frac{1}{(x^{2} + x)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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