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

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