There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {({x}^{16} + 3)}^{\frac{3}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{16} + 3)^{\frac{3}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x^{16} + 3)^{\frac{3}{2}}\right)}{dx}\\=&(\frac{3}{2}(x^{16} + 3)^{\frac{1}{2}}(16x^{15} + 0))\\=&24(x^{16} + 3)^{\frac{1}{2}}x^{15}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 24(x^{16} + 3)^{\frac{1}{2}}x^{15}\right)}{dx}\\=&24(\frac{\frac{1}{2}(16x^{15} + 0)}{(x^{16} + 3)^{\frac{1}{2}}})x^{15} + 24(x^{16} + 3)^{\frac{1}{2}}*15x^{14}\\=&\frac{192x^{30}}{(x^{16} + 3)^{\frac{1}{2}}} + 360(x^{16} + 3)^{\frac{1}{2}}x^{14}\\ \end{split}\end{equation} \]

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