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

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