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

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