There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{(sqrt(9{x}^{2} + 16) + 5x)}{4}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{4}sqrt(9x^{2} + 16) + \frac{5}{4}x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{4}sqrt(9x^{2} + 16) + \frac{5}{4}x\right)}{dx}\\=&\frac{\frac{1}{4}(9*2x + 0)*\frac{1}{2}}{(9x^{2} + 16)^{\frac{1}{2}}} + \frac{5}{4}\\=&\frac{9x}{4(9x^{2} + 16)^{\frac{1}{2}}} + \frac{5}{4}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{9x}{4(9x^{2} + 16)^{\frac{1}{2}}} + \frac{5}{4}\right)}{dx}\\=&\frac{9(\frac{\frac{-1}{2}(9*2x + 0)}{(9x^{2} + 16)^{\frac{3}{2}}})x}{4} + \frac{9}{4(9x^{2} + 16)^{\frac{1}{2}}} + 0\\=&\frac{-81x^{2}}{4(9x^{2} + 16)^{\frac{3}{2}}} + \frac{9}{4(9x^{2} + 16)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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