There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{4{(x + 1)}^{(\frac{5}{2})}}{15} - \frac{4{(x + 1)}^{(\frac{3}{2})}}{3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{4}{15}(x + 1)^{\frac{5}{2}} - \frac{4}{3}(x + 1)^{\frac{3}{2}}\right)}{dx}\\=&\frac{4}{15}((x + 1)^{\frac{5}{2}}((0)ln(x + 1) + \frac{(\frac{5}{2})(1 + 0)}{(x + 1)})) - \frac{4}{3}((x + 1)^{\frac{3}{2}}((0)ln(x + 1) + \frac{(\frac{3}{2})(1 + 0)}{(x + 1)}))\\=&\frac{2(x + 1)^{\frac{5}{2}}}{3(x + 1)} - \frac{2(x + 1)^{\frac{3}{2}}}{(x + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2(x + 1)^{\frac{5}{2}}}{3(x + 1)} - \frac{2(x + 1)^{\frac{3}{2}}}{(x + 1)}\right)}{dx}\\=&\frac{2(\frac{5}{2}(x + 1)^{\frac{3}{2}}(1 + 0))}{3(x + 1)} + \frac{2(x + 1)^{\frac{5}{2}}(\frac{-(1 + 0)}{(x + 1)^{2}})}{3} - \frac{2(\frac{3}{2}(x + 1)^{\frac{1}{2}}(1 + 0))}{(x + 1)} - 2(x + 1)^{\frac{3}{2}}(\frac{-(1 + 0)}{(x + 1)^{2}})\\=&(x + 1)^{\frac{1}{2}} - \frac{1}{(x + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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