There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{(x + 4)}{sqrt({x}^{2} + 4)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x}{sqrt(x^{2} + 4)} + \frac{4}{sqrt(x^{2} + 4)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x}{sqrt(x^{2} + 4)} + \frac{4}{sqrt(x^{2} + 4)}\right)}{dx}\\=&\frac{1}{sqrt(x^{2} + 4)} + \frac{x*-(2x + 0)*\frac{1}{2}}{(x^{2} + 4)(x^{2} + 4)^{\frac{1}{2}}} + \frac{4*-(2x + 0)*\frac{1}{2}}{(x^{2} + 4)(x^{2} + 4)^{\frac{1}{2}}}\\=&\frac{1}{sqrt(x^{2} + 4)} - \frac{x^{2}}{(x^{2} + 4)^{\frac{3}{2}}} - \frac{4x}{(x^{2} + 4)^{\frac{3}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{sqrt(x^{2} + 4)} - \frac{x^{2}}{(x^{2} + 4)^{\frac{3}{2}}} - \frac{4x}{(x^{2} + 4)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{-(2x + 0)*\frac{1}{2}}{(x^{2} + 4)(x^{2} + 4)^{\frac{1}{2}}} - (\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 4)^{\frac{5}{2}}})x^{2} - \frac{2x}{(x^{2} + 4)^{\frac{3}{2}}} - 4(\frac{\frac{-3}{2}(2x + 0)}{(x^{2} + 4)^{\frac{5}{2}}})x - \frac{4}{(x^{2} + 4)^{\frac{3}{2}}}\\=&\frac{-3x}{(x^{2} + 4)^{\frac{3}{2}}} + \frac{3x^{3}}{(x^{2} + 4)^{\frac{5}{2}}} + \frac{12x^{2}}{(x^{2} + 4)^{\frac{5}{2}}} - \frac{4}{(x^{2} + 4)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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