There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{16({(x + 1)}^{(\frac{3}{2})} - {x}^{(\frac{3}{2})})}{3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{16}{3}(x + 1)^{\frac{3}{2}} - \frac{16}{3}{x}^{\frac{3}{2}}\right)}{dx}\\=&\frac{16}{3}((x + 1)^{\frac{3}{2}}((0)ln(x + 1) + \frac{(\frac{3}{2})(1 + 0)}{(x + 1)})) - \frac{16}{3}({x}^{\frac{3}{2}}((0)ln(x) + \frac{(\frac{3}{2})(1)}{(x)}))\\=&\frac{8(x + 1)^{\frac{3}{2}}}{(x + 1)} - 8x^{\frac{1}{2}}\\ \end{split}\end{equation} \]

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