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

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