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

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