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

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