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

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