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

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