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

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