There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arctan(\frac{(4 + {x}^{2})}{(4 - {x}^{2})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arctan(\frac{x^{2}}{(-x^{2} + 4)} + \frac{4}{(-x^{2} + 4)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan(\frac{x^{2}}{(-x^{2} + 4)} + \frac{4}{(-x^{2} + 4)})\right)}{dx}\\=&(\frac{((\frac{-(-2x + 0)}{(-x^{2} + 4)^{2}})x^{2} + \frac{2x}{(-x^{2} + 4)} + 4(\frac{-(-2x + 0)}{(-x^{2} + 4)^{2}}))}{(1 + (\frac{x^{2}}{(-x^{2} + 4)} + \frac{4}{(-x^{2} + 4)})^{2})})\\=&\frac{2x^{3}}{(-x^{2} + 4)^{2}(\frac{x^{4}}{(-x^{2} + 4)^{2}} + \frac{8x^{2}}{(-x^{2} + 4)^{2}} + \frac{16}{(-x^{2} + 4)^{2}} + 1)} + \frac{2x}{(-x^{2} + 4)(\frac{x^{4}}{(-x^{2} + 4)^{2}} + \frac{8x^{2}}{(-x^{2} + 4)^{2}} + \frac{16}{(-x^{2} + 4)^{2}} + 1)} + \frac{8x}{(-x^{2} + 4)^{2}(\frac{x^{4}}{(-x^{2} + 4)^{2}} + \frac{8x^{2}}{(-x^{2} + 4)^{2}} + \frac{16}{(-x^{2} + 4)^{2}} + 1)}\\ \end{split}\end{equation} \]

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