There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(\frac{8x}{(2 + x)})}^{(9x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (\frac{8x}{(x + 2)})^{(9x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (\frac{8x}{(x + 2)})^{(9x)}\right)}{dx}\\=&((\frac{8x}{(x + 2)})^{(9x)}((9)ln(\frac{8x}{(x + 2)}) + \frac{(9x)(8(\frac{-(1 + 0)}{(x + 2)^{2}})x + \frac{8}{(x + 2)})}{(\frac{8x}{(x + 2)})}))\\=&9(\frac{8x}{(x + 2)})^{(9x)}ln(\frac{8x}{(x + 2)}) - \frac{9x^{2}(\frac{8x}{(x + 2)})^{(9x)}}{(x + 2)^{2}} - \frac{18x(\frac{8x}{(x + 2)})^{(9x)}}{(x + 2)^{2}} + \frac{9x(\frac{8x}{(x + 2)})^{(9x)}}{(x + 2)} + \frac{18(\frac{8x}{(x + 2)})^{(9x)}}{(x + 2)}\\ \end{split}\end{equation} \]

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