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

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