There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(3x + 1)}{(3{x}^{2} + 4x + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3x}{(3x^{2} + 4x + 1)} + \frac{1}{(3x^{2} + 4x + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{3x}{(3x^{2} + 4x + 1)} + \frac{1}{(3x^{2} + 4x + 1)}\right)}{dx}\\=&3(\frac{-(3*2x + 4 + 0)}{(3x^{2} + 4x + 1)^{2}})x + \frac{3}{(3x^{2} + 4x + 1)} + (\frac{-(3*2x + 4 + 0)}{(3x^{2} + 4x + 1)^{2}})\\=&\frac{-18x^{2}}{(3x^{2} + 4x + 1)^{2}} - \frac{18x}{(3x^{2} + 4x + 1)^{2}} + \frac{3}{(3x^{2} + 4x + 1)} - \frac{4}{(3x^{2} + 4x + 1)^{2}}\\ \end{split}\end{equation} \]

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