There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {({x}^{2} + \frac{1}{(8x)})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{2} + \frac{\frac{1}{8}}{x})^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x^{2} + \frac{\frac{1}{8}}{x})^{\frac{1}{2}}\right)}{dx}\\=&(\frac{\frac{1}{2}(2x + \frac{\frac{1}{8}*-1}{x^{2}})}{(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{1}{2}}})\\=&\frac{x}{(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{1}{2}}} - \frac{1}{16(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{1}{2}}x^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{x}{(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{1}{2}}} - \frac{1}{16(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{1}{2}}x^{2}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(2x + \frac{\frac{1}{8}*-1}{x^{2}})}{(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{3}{2}}})x + \frac{1}{(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(2x + \frac{\frac{1}{8}*-1}{x^{2}})}{(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{3}{2}}})}{16x^{2}} - \frac{-2}{16(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{1}{2}}x^{3}}\\=&\frac{-x^{2}}{(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{3}{2}}} + \frac{1}{8(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{3}{2}}x} + \frac{1}{8(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{1}{2}}x^{3}} - \frac{1}{256(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{3}{2}}x^{4}} + \frac{1}{(x^{2} + \frac{\frac{1}{8}}{x})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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