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

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