There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ x - {x}^{\frac{1}{2}}ln(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - x^{\frac{1}{2}}ln(x) + x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - x^{\frac{1}{2}}ln(x) + x\right)}{dx}\\=& - \frac{\frac{1}{2}ln(x)}{x^{\frac{1}{2}}} - \frac{x^{\frac{1}{2}}}{(x)} + 1\\=& - \frac{ln(x)}{2x^{\frac{1}{2}}} - \frac{1}{x^{\frac{1}{2}}} + 1\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{ln(x)}{2x^{\frac{1}{2}}} - \frac{1}{x^{\frac{1}{2}}} + 1\right)}{dx}\\=& - \frac{\frac{-1}{2}ln(x)}{2x^{\frac{3}{2}}} - \frac{1}{2x^{\frac{1}{2}}(x)} - \frac{\frac{-1}{2}}{x^{\frac{3}{2}}} + 0\\=&\frac{ln(x)}{4x^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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