There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{((1 + x)(2 + x))}{(x(1 + {x}^{2}))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{(x^{3} + x)} + \frac{3x}{(x^{3} + x)} + \frac{2}{(x^{3} + x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{(x^{3} + x)} + \frac{3x}{(x^{3} + x)} + \frac{2}{(x^{3} + x)}\right)}{dx}\\=&(\frac{-(3x^{2} + 1)}{(x^{3} + x)^{2}})x^{2} + \frac{2x}{(x^{3} + x)} + 3(\frac{-(3x^{2} + 1)}{(x^{3} + x)^{2}})x + \frac{3}{(x^{3} + x)} + 2(\frac{-(3x^{2} + 1)}{(x^{3} + x)^{2}})\\=& - \frac{3x^{4}}{(x^{3} + x)^{2}} - \frac{9x^{3}}{(x^{3} + x)^{2}} + \frac{2x}{(x^{3} + x)} - \frac{7x^{2}}{(x^{3} + x)^{2}} - \frac{3x}{(x^{3} + x)^{2}} + \frac{3}{(x^{3} + x)} - \frac{2}{(x^{3} + x)^{2}}\\ \end{split}\end{equation} \]

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