There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(\frac{(6x)}{(1 + x)})}^{(3x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (\frac{6x}{(x + 1)})^{(3x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (\frac{6x}{(x + 1)})^{(3x)}\right)}{dx}\\=&((\frac{6x}{(x + 1)})^{(3x)}((3)ln(\frac{6x}{(x + 1)}) + \frac{(3x)(6(\frac{-(1 + 0)}{(x + 1)^{2}})x + \frac{6}{(x + 1)})}{(\frac{6x}{(x + 1)})}))\\=&3(\frac{6x}{(x + 1)})^{(3x)}ln(\frac{6x}{(x + 1)}) - \frac{3x^{2}(\frac{6x}{(x + 1)})^{(3x)}}{(x + 1)^{2}} - \frac{3x(\frac{6x}{(x + 1)})^{(3x)}}{(x + 1)^{2}} + \frac{3x(\frac{6x}{(x + 1)})^{(3x)}}{(x + 1)} + \frac{3(\frac{6x}{(x + 1)})^{(3x)}}{(x + 1)}\\ \end{split}\end{equation} \]

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