There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{3}^{x}sin(3x)}{({9}^{x} - 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{3}^{x}sin(3x)}{({9}^{x} - 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{3}^{x}sin(3x)}{({9}^{x} - 1)}\right)}{dx}\\=&(\frac{-(({9}^{x}((1)ln(9) + \frac{(x)(0)}{(9)})) + 0)}{({9}^{x} - 1)^{2}}){3}^{x}sin(3x) + \frac{({3}^{x}((1)ln(3) + \frac{(x)(0)}{(3)}))sin(3x)}{({9}^{x} - 1)} + \frac{{3}^{x}cos(3x)*3}{({9}^{x} - 1)}\\=&\frac{-{9}^{(2x)}ln(9)sin(3x)}{({9}^{x} - 1)^{2}} + \frac{{3}^{x}ln(3)sin(3x)}{({9}^{x} - 1)} + \frac{3 * {3}^{x}cos(3x)}{({9}^{x} - 1)}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！