There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {({x}^{8} + 15)}^{\frac{5}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{8} + 15)^{\frac{5}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x^{8} + 15)^{\frac{5}{2}}\right)}{dx}\\=&(\frac{5}{2}(x^{8} + 15)^{\frac{3}{2}}(8x^{7} + 0))\\=&20(x^{8} + 15)^{\frac{3}{2}}x^{7}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 20(x^{8} + 15)^{\frac{3}{2}}x^{7}\right)}{dx}\\=&20(\frac{3}{2}(x^{8} + 15)^{\frac{1}{2}}(8x^{7} + 0))x^{7} + 20(x^{8} + 15)^{\frac{3}{2}}*7x^{6}\\=&240(x^{8} + 15)^{\frac{1}{2}}x^{14} + 140(x^{8} + 15)^{\frac{3}{2}}x^{6}\\ \end{split}\end{equation} \]

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