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

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