There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {({x}^{8} + 15)}^{\frac{3}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{8} + 15)^{\frac{3}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x^{8} + 15)^{\frac{3}{2}}\right)}{dx}\\=&(\frac{3}{2}(x^{8} + 15)^{\frac{1}{2}}(8x^{7} + 0))\\=&12(x^{8} + 15)^{\frac{1}{2}}x^{7}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 12(x^{8} + 15)^{\frac{1}{2}}x^{7}\right)}{dx}\\=&12(\frac{\frac{1}{2}(8x^{7} + 0)}{(x^{8} + 15)^{\frac{1}{2}}})x^{7} + 12(x^{8} + 15)^{\frac{1}{2}}*7x^{6}\\=&\frac{48x^{14}}{(x^{8} + 15)^{\frac{1}{2}}} + 84(x^{8} + 15)^{\frac{1}{2}}x^{6}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{48x^{14}}{(x^{8} + 15)^{\frac{1}{2}}} + 84(x^{8} + 15)^{\frac{1}{2}}x^{6}\right)}{dx}\\=&48(\frac{\frac{-1}{2}(8x^{7} + 0)}{(x^{8} + 15)^{\frac{3}{2}}})x^{14} + \frac{48*14x^{13}}{(x^{8} + 15)^{\frac{1}{2}}} + 84(\frac{\frac{1}{2}(8x^{7} + 0)}{(x^{8} + 15)^{\frac{1}{2}}})x^{6} + 84(x^{8} + 15)^{\frac{1}{2}}*6x^{5}\\=&\frac{-192x^{21}}{(x^{8} + 15)^{\frac{3}{2}}} + \frac{1008x^{13}}{(x^{8} + 15)^{\frac{1}{2}}} + 504(x^{8} + 15)^{\frac{1}{2}}x^{5}\\ \end{split}\end{equation} \]

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