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

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