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

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