There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {({x}^{8} + 15)}^{\frac{7}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{8} + 15)^{\frac{7}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x^{8} + 15)^{\frac{7}{2}}\right)}{dx}\\=&(\frac{7}{2}(x^{8} + 15)^{\frac{5}{2}}(8x^{7} + 0))\\=&28(x^{8} + 15)^{\frac{5}{2}}x^{7}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 28(x^{8} + 15)^{\frac{5}{2}}x^{7}\right)}{dx}\\=&28(\frac{5}{2}(x^{8} + 15)^{\frac{3}{2}}(8x^{7} + 0))x^{7} + 28(x^{8} + 15)^{\frac{5}{2}}*7x^{6}\\=&560(x^{8} + 15)^{\frac{3}{2}}x^{14} + 196(x^{8} + 15)^{\frac{5}{2}}x^{6}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 560(x^{8} + 15)^{\frac{3}{2}}x^{14} + 196(x^{8} + 15)^{\frac{5}{2}}x^{6}\right)}{dx}\\=&560(\frac{3}{2}(x^{8} + 15)^{\frac{1}{2}}(8x^{7} + 0))x^{14} + 560(x^{8} + 15)^{\frac{3}{2}}*14x^{13} + 196(\frac{5}{2}(x^{8} + 15)^{\frac{3}{2}}(8x^{7} + 0))x^{6} + 196(x^{8} + 15)^{\frac{5}{2}}*6x^{5}\\=&6720(x^{8} + 15)^{\frac{1}{2}}x^{21} + 11760(x^{8} + 15)^{\frac{3}{2}}x^{13} + 1176(x^{8} + 15)^{\frac{5}{2}}x^{5}\\ \end{split}\end{equation} \]

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