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

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