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

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