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

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