There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(\frac{7x}{(9 + x)})}^{(6x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (\frac{7x}{(x + 9)})^{(6x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (\frac{7x}{(x + 9)})^{(6x)}\right)}{dx}\\=&((\frac{7x}{(x + 9)})^{(6x)}((6)ln(\frac{7x}{(x + 9)}) + \frac{(6x)(7(\frac{-(1 + 0)}{(x + 9)^{2}})x + \frac{7}{(x + 9)})}{(\frac{7x}{(x + 9)})}))\\=&6(\frac{7x}{(x + 9)})^{(6x)}ln(\frac{7x}{(x + 9)}) - \frac{6x^{2}(\frac{7x}{(x + 9)})^{(6x)}}{(x + 9)^{2}} - \frac{54x(\frac{7x}{(x + 9)})^{(6x)}}{(x + 9)^{2}} + \frac{6x(\frac{7x}{(x + 9)})^{(6x)}}{(x + 9)} + \frac{54(\frac{7x}{(x + 9)})^{(6x)}}{(x + 9)}\\ \end{split}\end{equation} \]

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