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

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